I have a shy bladder. Much like others have mentioned, thinking about something else is the key for me. Typically, I think about the stuff that makes me worry, that I usually try NOT to think about. That usually works, but not always.
Well, it’s not so much I’m pee shy, honestly the peeing doesn’t bother me so much as the wiping.
I know I know, but it’s just something that I don’t want other folks to hear. I guess cuz it’s like they know what I’m wiping. I’m weird what can I say.
Although, I can’t pee in front of anyone. Husband, mother, bestfriend…no one. So I’ll have to pee while I’m asleep and end up having a dream that I’m tryiing to pee and someone is in the room with me while I’m trying to pee. TMI I know, but it keeps me from whizzing on myself everytime!
As others have already posted, the best solution is to not dwell on your surroundings. Clear your mind and think of another place. I think of a big flowing waterfall – works for me! 
I used to be pee shy, then I had sex for the first time…