It's easy for disk file, but harder for Bitmap in memory.
System.Drawing.Bitmap bmp;
Image image;
...
MemoryStream ms = new MemoryStream();
bmp.Save(ms, System.Drawing.Imaging.ImageFormat.Png);
ms.Position = 0;
BitmapImage bi = new BitmapImage();
bi.BeginInit();
bi.StreamSource = ms;
bi.EndInit();
image.Source = bi;