Hi  JOYSON,
There is no need of taking asp button for opening the modal onclick of it instead what you can do is take button element and set its attribute data-toggle="modal" data-target="#modalDivId" like so that there is no need of writing extra code of jquery or anything else.
I have created a sample which full fill your requirement you need to modify the code according to your need.
HTML
<div>
    <button type="button" class="btn btn-info btn-lg" data-toggle="modal" data-target="#myModal">
        Open Modal</button>
    <div id="myModal" class="modal fade" role="dialog">
        <div class="modal-dialog" style="width: 400px;">
            <div class="modal-content">
                <div class="modal-header">
                    <button type="button" class="close" data-dismiss="modal">
                        ×</button>
                    <h4 class="modal-title">
                        Login</h4>
                </div>
                <div class="modal-body">
                    <table>
                        <tr>
                            <td>
                                <span class="text-danger">UserName: </span>
                            </td>
                            <td>
                                <asp:TextBox ID="txtUserName" CssClass="form-control" Width="250px" runat="server" />
                            </td>
                        </tr>
                        <tr>
                            <td>
                                <span class="text-danger">Password: </span>
                            </td>
                            <td>
                                <asp:TextBox ID="txtPassword" CssClass="form-control" Width="250px" runat="server" />
                            </td>
                        </tr>
                    </table>
                </div>
                <div class="modal-footer" style="text-align: center">
                    <button id="btnSave" type="button" class="btn btn-primary" data-dismiss="modal">
                        Save</button>
                    <button type="button" class="btn btn-default" data-dismiss="modal">
                        Close</button>
                </div>
            </div>
        </div>
    </div>
</div>
<div>
    <style type="text/css">
        body
        {
            font-family: Arial;
            font-size: 10pt;
        }
        table
        {
            border: 0px solid #ccc;
        }
        table th
        {
            background-color: #F7F7F7;
            color: #333;
            font-weight: bold;
        }
        table th, table td
        {
            padding: 5px;
        }
    </style>
    <script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js"></script>
    <script type="text/javascript" src="http://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js"></script>
    <link rel="stylesheet" href="http://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css" />
    <script type="text/javascript">
        $(function () {
            $('[id*=btnSave]').click(function () {
                var UserDetail = {};
                UserDetail.UserName = $('[id*=txtUserName]').val();
                UserDetail.Password = $('[id*=txtPassword]').val();
                $.ajax({
                    type: "POST",
                    url: "Default.aspx/UserDetails",
                    data: '{UserDetail :' + JSON.stringify(UserDetail) + '}',
                    contentType: "application/json; charset=utf-8",
                    dataType: "json",
                    success: function (response) {
                        alert(response.d);
                    },
                    failure: function (response) {
                        alert(response.responseText);
                    },
                    error: function (response) {
                        alert(response.responseText);
                    }
                });
            });
        });
    </script>
</div>
C#
[WebMethod]
public static string UserDetails(UserDetail UserDetail)
{
    //your saving code comes here.
    return "Data Saved Successfully";
}
public class UserDetail
{
    public string UserName { get; set; }
    public string Password { get; set; }        
}
VB.Net
<WebMethod> _
Public Shared Function UserDetails(UserDetail As UserDetail) As String
	'your saving code comes here.
	Return "Data Saved Successfully"
End Function
Public Class UserDetail
	Public Property UserName() As String
		Get
			Return m_UserName
		End Get
		Set
			m_UserName = Value
		End Set
	End Property
	Private m_UserName As String
	Public Property Password() As String
		Get
			Return m_Password
		End Get
		Set
			m_Password = Value
		End Set
	End Property
	Private m_Password As String
End Class
ScreenShot
