Should I approach sponsors at trade shows or will I be bothering them?

Yes, you should approach sponsors at trade shows. According to John Viscardo from Hoonigan, you should 'bother the hell out of the marketing people at trade shows.' While they're not there specifically to talk to every racer, it's part of the sales pitch process. If possible, book an appointment beforehand, but if not, introduce yourself, shake their hand, and make an impression. You don't need to give them a full sponsorship deck since they won't have room for it on the flight home, but use trade shows as a touch point to start relationships that you can follow up on later.