Well I am no expert by any means, but you said your pup seems to bite more when she's excited or when you are playing with her, right?
How do you "play"? Puppies should not be encouraged to participate in rough play, as it encourages aggression. Yours will grow up to be a "large" dog, so this behavior needs to be curbed asap. If your play includes tug-o-war or play fighting, stop and try to stick to playing with a ball, or fetch maybe.
Also, encourage her to be in a calm state of mind as often as possible. Try to retain a "calm, assertive" energy at all times as your pup will feed off of YOUR energy.
One of the most common things I've noticed is people start talking in that high-pitched, "oooh aren't you such a cuuuute good wittle doggie!" voice. There are ways to show your dog affection without working the poor pooch into a frenzy. Think about it... when you do this, you're putting that dog into another frame of mind - the overstimulated, hyperactive dog, which, if not everyone's in the mood for, can be a nuisance. Then 5 minutes later when you're ready for "calm dog" state you expect them to suddenly relax again, mostly without communicating this the proper way. This isn't fair to your dog.
Dogs are smart and can read us better than we sometimes know. Our energy and actions can speak much louder to dogs than words, I've found.
Last but not least I think maybe your pup doesn't respect you as her pack leader. With other dogs, she knows what's up, but maybe you haven't shown her the proper chain of command. YOU are in charge, don't let her actions control you. Maybe it would be a good idea to practice "dominant" positions with your pup, to start giving her the idea that this biting (aka .. challenging you?) will not be tolerated. Don't lay down or let her assert herself over you. If she starts her biting actions, flip her over and lay her on her back with her belly up to you. (In dog language this is a submissive act) It may also help to stand directly over her as you have her do this.
I've had issues with my pitbull pup who we adopted from the local animal shelter, and he came with his own slew of "bad habits" as well as dominance issues. It's taken quite a bit of patience as well as some time, but keeping an assertive, and calm (this is soo important) frame of mind has helped tremendously.
I think mostly it's about letting them know what's up. You are the leader, first and foremost. When you get that part down... the rest will come naturally. Wish you and your pup the best of luck.... hope I was able to shed some helpful light. =)