예전에 어디선가 갈무리했던 팁인데 오래간만에 꺼내보내요 ^^
Image1.Picture.Bitmap.SaveToFile('bmp파일명') 으로 저장하시면 될 듯...


procedure TForm1.Button1Click(Sender: TObject);
var
   newBitmap: TBitmap;
   ScreenDC: HDC;
   REOrg: TPoint;
begin
   newBitmap := TBitmap.Create;
   try
      Image1.Picture.Graphic:=newBitmap;
      Image1.Picture.Graphic.Width := RichEdit1.ClientWidth;
      Image1.Picture.Graphic.Height := RichEdit1.ClientHeight;
      REOrg:=RichEdit1.ClientToScreen(Point(0,0));
      ScreenDC:=GetDC(0);
      try
         BitBlt(Image1.Picture.Bitmap.Canvas.Handle,0,0,RichEdit1.ClientWidth, RichEdit1.ClientHeight,ScreenDC,REOrg.X, REOrg.Y, SRCCOPY);
      finally
         ReleaseDC(0, ScreenDC);
      end;
   finally
      newBitmap.Free;
   end;
end;

감사 합니다 고수님...