She might be biting her tail becuase a tick or a flea got on the tail. If she is trying to play with her tail by biting it, redirect her attention to a toy of a chew stick. If it something due to her having fleas or ticks, I would use a flea or tick shampoo and wash her tail in it when you usually wash her and have you been giving her any parasite treatment meds like AvantX(I believe that is how you spell it?).
I agree you should try a flea and tick bath first. My mother being a groomer though has always said before you wet the dog lather the soap real thick on a dry dog around the ears and neck as well as the tail. Because if they are fleas once the water hits the dogs body the fleas will run to where they can hide from the water. By putting the soap on a dry dog the fleas will get stuck in the shampoo.
Huh I never knew that. What I usually do is spray the dog down with luke warm water, using that I have a moveable shower head so I have some what easy access for giving her a bath except for the fact that the head doesn't reach that far so I have to move the dog closer to the head to reach all parts of her body.
If it is ticks it is not such a big deal to get them wet but fleas will run to a dry safe place which is usually in the ears and under the tail. Once the dog is done with there bath they will run wild again. But if you do find fleas you then need to bomb your house and another trick to assist in killing the eggs left behind is to put mothballs in your vacuum bag or canister. That will help as well.
No it's not bad for dogs to bite their tail. It's just a sign that they are either bored...or maybe they are just itchy there. My dog does the same thing except to her lower left thigh...just in case though: Sift through it's fur to make sure there isn't any fleas or ticks.