If you can't get this corrected there is a good chance she will be put down eventually by someone. I think the behaviorist is a must in this case. Some dogs just have a mean streak. We had one a rescue that was fairly vicious for 2 years before becoming the best of all our dogs ever.
How do you know she likes to live outside? Does she sleep outside? Maybe she feels not part of the pack and is acting out.
Others will have better advice than me but please do not take your puppy on a mile long bike ride. That's just asking for hip and joint problems later.