Try this :) It saves the bitmap first into a memorystream and that writes it to a filestream (read: to the original file).
MemoryStream ms = new MemoryStream();
Bitmap myBitmap = new Bitmap(Path);
Graphics g = Graphics.FromImage(myBitmap);
StringFormat strFormat = new StringFormat();
strFormat.Alignment = StringAlignment.Center;
g.DrawString(Text, new Font("Tahoma", 20), Brushes.Black, new RectangleF(0, 0, 500, 500), strFormat);
myBitmap.Save(ms, myBitmap.RawFormat);
FileStream fs = new FileStream(Path, FileMode.Create);
ms.WriteTo(fs);
fs.Close();