My problem is that I can't keep the bag under my arm for very long at all. It starts to slip the moment I start playing. Help!
This is fairly common problem for pipers. It could be that your pipe bag is too large. Most people would do best with a small bag. If you are tall you might think about a medium size bag. (Only very tall should play a large bag, if anyone.) It could be that your blowpipe is too long. If you feel you have to stretch your neck to reach your blowpipe, it's probably too long and you ought to try a shorter one.
Even if your pipe bag and blowpipe are the perfect size, it could be that your bag cover is too loose or too slippery. A loose bag cover can be adjusted with a needle and thread (or get a smaller one) and slippery material can be fixed with some non-slip material from dycem.
Visit the Dycem home page. You'll want to get a non-slip reel in the color of your choice. Then you have to sew it on your bag cover.
Highland Gear makes nice covers and they can install dycem patches for you on both sides (arm side and body side).