Legally, I think that singing the bath would mean that you are at least entertaining yourself....

Should this not be the case and singing the bath be allowed, would you need a license if you took your bath in front of an audience and received money for it? And what changes would have to be made if this were allowed?

No, on further thought, I think that there should be licensed bathing, also. You Can't Be Too Careful These Days, you know.