Hi ilanocf,
For Carousel you have to use repeater control.
Please refer below sample.
Database
CREATE TABLE [dbo].[YoutubeVideos]
(
    [VideoId] [int] NOT NULL,
    [VideoUrl] [nvarchar](1000) NOT NULL
)
HTML
C#
<body class="container">
    <form id="form1" runat="server">
        <div id="myCarousel" class="carousel slide" data-ride="carousel" data-interval="false">
            <asp:Repeater ID="rptMain" runat="server" OnItemDataBound="OnItemDataBound">
                <ItemTemplate>
                    <ol class="carousel-indicators">
                        <asp:Repeater ID="rptIndicators" runat="server">
                            <ItemTemplate>
                                <li data-target="#myCarousel" data-slide-to='<%# Container.ItemIndex%>' class='<%# Container.ItemIndex == 0 ? "active" : "" %>'>
                                    <%# Container.ItemIndex + 1 %>
                                </li>
                            </ItemTemplate>
                        </asp:Repeater>
                    </ol>
                    <div class="carousel-inner" role="listbox">
                        <asp:Repeater ID="rptSlides" runat="server">
                            <ItemTemplate>
                                <div <%# Container.ItemIndex == 0 ? "class=\"item active\"" : "class=\"item\"" %>>
                                    <iframe id="video" height="300" frameborder="0" allowfullscreen
                                        src='<%# "https://www.youtube.com/embed/" + DataBinder.Eval(Container, "DataItem.VideoUrl").ToString().Split(new string[] {"v="}, StringSplitOptions.None)[1] %>'></iframe>
                                </div>
                            </ItemTemplate>
                        </asp:Repeater>
                    </div>
                </ItemTemplate>
            </asp:Repeater>
            <a class="left carousel-control" href="#myCarousel" role="button" data-slide="prev">
                <span class="glyphicon glyphicon-chevron-left" aria-hidden="true"></span><span class="sr-only">Previous</span>
            </a>
            <a class="right carousel-control" href="#myCarousel" role="button" data-slide="next">
                <span class="glyphicon glyphicon-chevron-right" aria-hidden="true"></span><span class="sr-only">Next</span>
            </a>
        </div>        
    </form>
</body>
VB.Net
<body class="container">
    <form id="form1" runat="server">
        <div id="myCarousel" class="carousel slide" data-ride="carousel" data-interval="false">
            <asp:Repeater ID="rptMain" runat="server" OnItemDataBound="OnItemDataBound">
                <ItemTemplate>
                    <ol class="carousel-indicators">
                        <asp:Repeater ID="rptIndicators" runat="server">
                            <ItemTemplate>
                                <li data-target="#myCarousel" data-slide-to='<%# Container.ItemIndex%>' class='<%# If(Container.ItemIndex = 0, "active", "") %>'>
                                    <%# Container.ItemIndex + 1 %>
                                </li>
                            </ItemTemplate>
                        </asp:Repeater>
                    </ol>
                    <div class="carousel-inner" role="listbox">
                        <asp:Repeater ID="rptSlides" runat="server">
                            <ItemTemplate>
                                <div class='<%# If(Container.ItemIndex = 0, "item active", "item") %>'>
                                    <iframe id="video" height="300" frameborder="0" allowfullscreen
                                        src='<%# "https://www.youtube.com/embed/" + DataBinder.Eval(Container, "DataItem.VideoUrl").ToString().Split(New String() {"v="}, StringSplitOptions.None)(1) %>'></iframe>
                                </div>
                            </ItemTemplate>
                        </asp:Repeater>
                    </div>
                </ItemTemplate>
            </asp:Repeater>
            <a class="left carousel-control" href="#myCarousel" role="button" data-slide="prev">
                <span class="glyphicon glyphicon-chevron-left" aria-hidden="true"></span><span class="sr-only">Previous</span>
            </a>
            <a class="right carousel-control" href="#myCarousel" role="button" data-slide="next">
                <span class="glyphicon glyphicon-chevron-right" aria-hidden="true"></span><span class="sr-only">Next</span>
            </a>
        </div>
    </form>
</body>
Script and CSS
    <script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
    <link rel="stylesheet" media="screen" href='https://maxcdn.bootstrapcdn.com/bootstrap/3.3.5/css/bootstrap.min.css' />
    <script type="text/javascript" src='https://maxcdn.bootstrapcdn.com/bootstrap/3.3.5/js/bootstrap.min.js'></script>
    <style type="text/css">
            .carousel-indicators li {
                text-indent: 0 !important;
                height: 25px !important;
                width: 25px !important;
                line-height: 25px !important;
                border-radius: 25px !important;
                background-color: #d1d1d1;
                color: #444;
                text-align: center;
            }
                .carousel-indicators li.active {
                    background-color: #fff;
                }
            .carousel-inner .active.left {
                left: -33%;
            }
            .carousel-inner .active.right {
                left: 33%;
            }
            .carousel-inner .next {
                left: 33%
            }
            .carousel-inner .prev {
                left: -33%
            }
            .carousel-control.left {
                background-image: none;
            }
            .carousel-control.right {
                background-image: none;
            }
            .carousel-inner .item {
                background: white;
            }
            .carousel-inner .active {
                padding-left: 110px !important;
            }
            iframe {
                padding-left: 5px;
            }
    </style>
    <script type="text/javascript">
        $(function () {
            $('#myCarousel').carousel();
            $('.carousel .item').each(function () {
                var next = $(this).next();
                if (!next.length) {
                    next = $(this).siblings(':first');
                }
                next.children(':first-child').clone().appendTo($(this));
                if (next.next().length > 0) {
                    next.next().children(':first-child').clone().appendTo($(this));
                }
                else {
                    $(this).siblings(':first').children(':first-child').clone().appendTo($(this));
                }
            });
        });
    </script>
Namespaces
C#
using System.Data;
using System.Data.SqlClient;
using System.Configuration;
VB.Net
Imports System.Data
Imports System.Data.SqlClient
Imports System.Configuration
Code
C#
protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        DataTable dummy = new DataTable();
        dummy.Columns.Add();
        dummy.Rows.Add();
        rptMain.DataSource = dummy;
        rptMain.DataBind();
    }
}
protected void OnItemDataBound(object sender, RepeaterItemEventArgs e)
{
    if (e.Item.ItemType == ListItemType.Item || e.Item.ItemType == ListItemType.AlternatingItem)
    {
        Repeater rptIndicators = e.Item.FindControl("rptIndicators") as Repeater;
        Repeater rptSlides = e.Item.FindControl("rptSlides") as Repeater;
        rptIndicators.DataSource = GetData();
        rptIndicators.DataBind();
        rptSlides.DataSource = GetData();
        rptSlides.DataBind();
    }
}
private DataTable GetData()
{
    string constr = ConfigurationManager.ConnectionStrings["constr"].ConnectionString;
    using (SqlConnection con = new SqlConnection(constr))
    {
        using (SqlCommand cmd = new SqlCommand("SELECT VideoId, VideoUrl FROM YoutubeVideos", con))
        {
            using (SqlDataAdapter sda = new SqlDataAdapter(cmd))
            {
                DataTable dt = new DataTable();
                sda.Fill(dt);
                return dt;
            }
        }
    }
}
VB.Net
Protected Sub Page_Load(ByVal sender As Object, ByVal e As EventArgs) Handles Me.Load
    If Not Me.IsPostBack Then
        Dim dummy As DataTable = New DataTable()
        dummy.Columns.Add()
        dummy.Rows.Add()
        rptMain.DataSource = dummy
        rptMain.DataBind()
    End If
End Sub
Protected Sub OnItemDataBound(ByVal sender As Object, ByVal e As RepeaterItemEventArgs)
    If e.Item.ItemType = ListItemType.Item OrElse e.Item.ItemType = ListItemType.AlternatingItem Then
        Dim rptIndicators As Repeater = TryCast(e.Item.FindControl("rptIndicators"), Repeater)
        Dim rptSlides As Repeater = TryCast(e.Item.FindControl("rptSlides"), Repeater)
        rptIndicators.DataSource = GetData()
        rptIndicators.DataBind()
        rptSlides.DataSource = GetData()
        rptSlides.DataBind()
    End If
End Sub
Private Function GetData() As DataTable
    Dim constr As String = ConfigurationManager.ConnectionStrings("constr").ConnectionString
    Using con As SqlConnection = New SqlConnection(constr)
        Using cmd As SqlCommand = New SqlCommand("SELECT VideoId, VideoUrl FROM YoutubeVideos", con)
            Using sda As SqlDataAdapter = New SqlDataAdapter(cmd)
                Dim dt As DataTable = New DataTable()
                sda.Fill(dt)
                Return dt
            End Using
        End Using
    End Using
End Function
Screenshot
