<input type="button" id="BtnShowModal" name="BtnShowModal" class="btn btn-primary" data-toggle="modal" data-target="#modal-BtnShowModal" value="モーダル表示" onserverclick="BtnShowModal_Click" runat="server" />

<div class="modal" id="modal-BtnShowModal" tabindex="-1" data-keyboard="false" data-backdrop="static">
<div class="modal-dialog">
    <div class="modal-content">
        <div class="modal-header">
            <h4 class="modal-title" id="modal-label">タイトル</h4>
        </div>

        <asp:UpdatePanel ID="UpdatePanel2" runat="server">
        <ContentTemplate>
            <div class="modal-body" style="height: 400px;">
                <asp:GridView ID="gvData" runat="server" AutoGenerateColumns="False">
                <Columns>
                </Columns>
                </asp:GridView>
            </div>
        </ContentTemplate>
        </asp:UpdatePanel>

        <div class="modal-footer">
            <button type="button" class="btn btn-default" data-dismiss="modal">閉じる</button>
            <asp:Button ID="BtnSave" runat="server" Text="保存" OnClick="BtnSave_Click" />
        </div>
    </div>
</div>

protected void BtnShowModal_Click(object sender, EventArgs e)
{

}