I managed a tanning salon for two years. It is pretty gross the stuff that goes on there. But, you should just make sure that the place you tan is really clean and that the acrylic on the beds is really clean. All salons are required to use a certain type of cleaner that will kill all the gross stuff, so just look at the acrylic before you lay down and make sure that there is nothing on it. You can also look at the top of the bed.
Chances are that if the tanning room is clean (i.e. floors vacuumed, no lotion on walls, top of bed isn't dusty, stuff like that) then the bed is probably really clean also. Good luck!