Your baby sounds like my Esme. She is also a bitter. She bites because she wants to play, and for some reason she thinks biting=playing.
It has gotten better BUT it's still a problem. Every day I pray for her adult teeth because these puppy teeth are sooo sharp and hurt A LOT.
This is what I have done. Most of these things have not worked for Esme though.
Firm No
Clapping my hands
Saying ouch really loud
Time out
Shaker can (water bottle filled with pennies) -when she bites I shake it.
Holding her mouth closed and saying 'no bite!' (I know, awful, but I was desperate)
Tapping her nose
Flipping her on her back and growling at her (pure desperation)
Giving her something she CAN bite on (this works short term)
Like I said, most of these things haven't worked, BUT it HAS gotten better. She is now 5 1/2 months old.
Good Luck!