When a child has to wear a splint on their finger it is hard for them to bathe and shower, because you dont want them to get the dressing wet.  I tried taping a plastic bag over my daughter Cheyennes hand during her broken finger weeks, and it leaked everytime

with the exception of waterproof tape, that hurt her to take off.   That hand that was bandaged also seemed to get dirtier than the other, and it is hard to clean around the finger splint and tape.  I went and bought extra splints, and had my daughter bathe as normal, without putting the plastic bag over her splint, wash her hand as best she could, and since she was able to get it wet made it alot easier, then when she was all finished with her bath I dried her hand before taking the old tape and splint off, removed the tape, which was alot easier on her since it was wet, had her set her injured hand on a towel, used the blow dryer on cool/low and gently dried her hand, then put the new splint and tape on.  This way I can rotate splints, and beleive me they need a good cleaning!  SMELLY! lol.  I know this wont work for a cast, or if your child has stitches, but for just a broken finger it worked great. 

UPDATE, DONT!  PLEASE READ MY RESPONSE BELOW.  WILL REEDIT LATER.....

As per request....

The dr said that after a few weeks it was fine to change the splint while bathing, that it is no different than changing the tape every few days, and that as long as they are wearing the splint while bathing and put on a dry one that is fine.  I didnt cause her finger not to heal properly, it was not imobilized correctly to begin with, so after a few more weeks in a better splint, one that went half way up to her elbow she is now fine.  Thanks to all!!!