C# Converting 32bpp image to 8bpp

I'm trying to convert a 32bpp screenshot image to an 8bpp (or 4bpp, or 1bpp) format using C#. I've already looked at several stackoverflow answers on similar subjects and most suggest variations using the following code:

public static Bitmap Convert(Bitmap oldbmp) 
{
    Bitmap newbmp = new Bitmap(oldbmp.Width, oldbmp.Height, PixelFormat.Format8bppIndexed);

    Graphics gr = Graphics.FromImage(newbmp);

    gr.PageUnit = GraphicsUnit.Pixel;
    gr.DrawImageUnscaled(oldbmp, 0, 0);

    return newbmp;
}

However, when this executes, I get a the exception: A graphics object cannot be created from an image that has an indexed pixel format. I understand that 8, 4 and 1bpp images have colour table mappings rather than the actual colour pixels themselves (as in 32 or 16bpp images) so I assume I'm missing some conversion step somewhere, but I'm fairly new to C# (coming from a C++ background) and would prefer to be able do this using native C# calls rather than resorting to PInvoking BitBlt and GetDIBits etc. Anybody able to help me solve this? Thanks.

EDIT: I should point out that I need this to be backwardly compatible to .NET framework 2.0