here's a similar situation...
I travel in china with a group of about 6 coworkers....I deathly was afraid of going down to the sauna in the evening in fear of running into one of my co-workers , so I ended up ordering room service....
Running into a co-worker in the sauna would have been really really uncomfortable.
Now, the problem with sauna room service is that the mama brings up 2 girls at a time...In the sauna, you get to choose from 5 girls
I also made it a point to be on different floors from my co-workers