Bison is a very difficult character to learn in Super Street Fighter 2 Turbo because of how precise your inputs need to be in order to perform his combos. This POV video with an arcade stick should give you a good idea on how to do it.
Keep in mind that muscle memory is very useful for fighting games because you need to be able to do this without having to think about it. Professional street fighter players practice just like a martial artist would do by performing the same move thousands of times until they get it right.
The video was done with the Madcatz Arcade Stick round 1.