The rushing sounds like adrenalin to me. I had a bass player once who was really nervous on stage and pushed everything up to literally double speed! Remember to breathe and listen to yourself and (more importantly) the other band members. My timing tends to wander too and all of the other advice sounds excellent. Personally I had to learn when I used drum machines for a while. Frankly I hated the result, but once you can do it then you allow yourself to put some "soul" back in deliberately.