@ryanc OK, I have actually done this (with a t-shirt under another t-shirt, but the same principle applies). First get rid of the straps by unclipping them or by Flashdancing them down. Now you have made a tube you can wiggle out of. Here's how.
1. Pull bra away from ribs at the left side, using your right hand.
2. Pull your left arm inside your shirt.
3. Wedge your left elbow into and through the bra tube.
4. Pull the bra tube over your left arm so that the bra is now hiked up on your shoulder.
5. Put your left arm back out of the left sleeve.
6. Repeat the process (steps 1-5) for the others side.
7. The bra tube is now around your neck, and you should be able to pull it over your head.