Create a bitmap with the new size you want
Copy the original image at the top of the new bitmap
Write the text you want onto the new bitmap
Something like this: (untested)
var bmp = Bitmap.FromFile("orig.jpg");
var newImage = new Bitmap(bmp.Width, bmp.Height + 50);
var gr = Graphics.FromImage(newImage);
gr.DrawImageUnscaled(bmp, 0, 0);
gr.DrawString("this is the added text", SystemFonts.DefaultFont, Brushes.Black ,
new RectangleF(0, bmp.Height, bmp.Width, 50));
newImage.Save("newImg.jpg");
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