Assuming it is fully visible, then just use the form properties:
Bitmap printscreen = new Bitmap(Width,Height);
Graphics graphics = Graphics.FromImage(printscreen as Image);
graphics.CopyFromScreen(Left, Top, 0, 0, Size);
printscreen.Save(@"F:\Temp\screen.jpg", System.Drawing.Imaging.ImageFormat.Jpeg);
Will capture just the area you want of the form your button is in.