I compete in a double denim shirt. But I can bench more now without a shirt than I could 8 months ago with a shirt, and let me tell you, I get a lot out of a shirt. Things that make you stronger, like good exercises, increasing bar speed, increasing maximal strength, will benefit you whether you wear a poly shirt, a denim shirt, single layer, double layer, or no shirt at all. If you don't get stronger, your bench will not go up, shirt, raw, whatever.
Work in the different board presses on max effort day. Getting the bar off your chest is often a product of bar speed, and the ability to stay tight in the bottom of the lift. To get the bar off the chest as fast as possible, train for speed, and get your lats and upper back built up. Also do a lot of work for your rotators.