What is used to bind acrylic paint to the painting surface?

You don't really need anything to bind acrylic to common painting surfaces. Acrylic paintings (non-alla prima) made on illustration board are often made by using a thin acrylic wash to fix a line drawing to the board. The painting is then built up in layers. The reason to gesso a stretched canvas is two-fold. One reason is to seal the surface, but the other is to secure and tighten the canvas upon the stretcher bars. Therefore, if working on canvas board, a thin acrylic wash will do you just fine.