I wrap tape from the bottom, starting on the bottom and making a full turn before starting up the bar. I wrap the right bar counter-clockwise looking from behind the bike. End at the top, cutting a triangle out of the last inch and a half and finishing right behind the brake cable. Wrap 2 or 3 loops of quality electrical tape in the same direction, ending again just behind the brake cable. Very seldom do those wraps come loose.

Edit: I am not kind to tape. I ride uphill hard out of the saddle, sometimes in huge gears. The details of wrap direction make a big difference for me. It sounds like you wrapped yours in the opposite direction which I would loosen at the top climbing with my hands close on the tops.

Ben