Someone at work has bed bugs, should I treat my clothes as a precaution?

Your choice. If his clothing is near his bed at night - a bed bug can hop on. Cimex lectularius or the bed bug is a parasite that is nocturnal. It can be transported on your clothing, luggage, second hand furniture etc. You can even get it using public transportation. It can go up to a year without feeding, so that allows it to just sit and wait until it catches a ride on something or someone. It is an >>>.
Bed bugs. Mites are present in every. It is unlikely that he will carry these mites to the point of infestation if he has a daily shower. I doubt very much that he would infect you with his bed bugs.