If your are content with a fixed height and assuming you are using a solid background as Starpulse only with your logo....
1) Create a *.PNG file with a white background, only make the image width wider than any of the pictures you plan on watermarking - 50px high by 1024px wide, for example. Paste your logo in the center of it and save it.
2) Download a free program called FastStone Photo Resizer. Load the file above into the watermarking option and position it as bottom-center then do your batch. You can also use the canvas size option to add the extra space of the watermark image to the bottom of the pictures so the watermark doesn't take away from the image content.