Carry dental floss with you, and discreetly excuse yourself to the restroom. I think that's a pretty common problem.

I also know that teeth can be moved around with time. If the teeth are in a reachable and easily accessible spot, try gently prying them apart. Use something soft, but firm like a Popsicle stick, and every day for a few seconds, use it to push your teeth apart. I had a dentist tell me to do this to correct an minor under-bite once