There is no direct way to interact between directx and GDI. When i encoutered this same problem i resorted to readying out the bytes from GDI to memory and then back to direct3D. I added my code below, it should work since i think it is being used in my project :) 
Note this is for directx11 (should be easily converted). Also, usage of *B*GRA texture format is intentional, otherwise colors are inverted.
If you need more performance, i suggest you look into DirectDraw.
    private byte[] getBitmapRawBytes(Bitmap bmp)
{
    Rectangle rect = new Rectangle(0, 0, bmp.Width, bmp.Height);
    System.Drawing.Imaging.BitmapData bmpData =
        bmp.LockBits(rect, System.Drawing.Imaging.ImageLockMode.ReadWrite, PixelFormat.Format32bppArgb);
    // Get the address of the first line.
    IntPtr ptr = bmpData.Scan0;
    // Declare an array to hold the bytes of the bitmap.
    int bytes = Math.Abs(bmpData.Stride) * bmp.Height;
    byte[] rgbValues = new byte[bytes];
    // Copy the RGB values into the array.
    System.Runtime.InteropServices.Marshal.Copy(ptr, rgbValues, 0, bytes);
    // Unlock the bits.
    bmp.UnlockBits(bmpData);
    return rgbValues;
}
/// <summary>
/// The bitmap and the texture should be same size.
/// The Texture format should be B8G8R8A8_UNorm
/// Bitmap pixelformat is read as PixelFormat.Format32bppArgb, so if this is the native format maybe speed is higher?
/// </summary>
/// <param name="bmp"></param>
/// <param name="tex"></param>
public void WriteBitmapToTexture(Bitmap bmp, GPUTexture tex)
{
    System.Diagnostics.Debug.Assert(tex.Resource.Description.Format == Format.B8G8R8A8_UNorm);
    var bytes = getBitmapRawBytes(bmp);
    tex.SetTextureRawData(bytes);
}