If this biting problem keeps on you have 2 answers now. 1 is to find another piano teacher or maybe get particular classes so that th epiano teacher comes to you nad not you to him/her. The other thing is you could sue your teacher. I think is against the law to have a agressive dog speacially if it has bitten other people. I know this might be more expensive 'cause then you'll have to get a lawyer. i recommend that you get another piano teacher.