Can I put just a small image on a garment? Is it cheaper?

We print the fabric first, then cut and sew, so the entire garment surface is printed, including the area around your image. That surrounding area takes whatever background colour you build into your artwork; it is not left blank or white by default, so set the background colour you want in your file. And because the whole surface is printed either way, the price is identical whether you use a small central image or a full bleed.