Apart from aero tubing, specific TT bikes usually have a slightly longer wheelbase, and sometimes a slacker head-tube angle, both which make the steering more stable, therefore the bike is more likely to hold a dead straight line with the sllightly less control the rider has using aero bars.
BUT, there's noting wrong with adapting a 'normal' bike for time trials. Aero testing shows that body position is the MAJOR OVERWHELMING factor when it comes to aerodynamics, and wheels is a very distant second. All the rest -- aero tubing, etc -- is minimal. I've read stuff saying that a tight, non-flapping clothing is more important than aero wheels, but I'm not sure about that one. 🙂
check out how body position affects speed:
http://www.legslarry.beerdrinkers.co.uk/tech/SpeedAndPower.htm
According to Hed, a "typical" 150lb rider in 'normal' conditions generates 6.5lbs of drag, and the best aero wheels reduce the drag to ~6.25 lbs