When you wrap from the top down your hand catches on the exposed edges of the tape as it tends to slide down and toward the outside of the handlebar. Wrapping from the bottom up cures that problem.

If you start from the bottom of the bar, pull the wrap up and toward the outside. That way as you grasp the bar you will tend to tighten rather than loosen the bar wrap.

There is a knack for how much tension to use when wrapping bars. If you're using Cinelli cork, for example, you want to pull it until it ALMOST breaks. That feel only comes with practice. A couple of times, I've used a little too much tension. Then you have to utter some words that only bicycle mechanics are allowed to say and go buy a new package of bar wrap.