College credit would be determined by the AP test regardless of classes taken (assuming that it counts for your college), so that shouldn't be a consideration. You can take the BC test whether or not you've taken the BC class. Honestly, I would say it depends on the teaching staff at your school. I personally found pretty much every math class from 4th grade onward boring until Calculus AB, which I maintain to have been the best math class I took until college, but your school might be different.
The Calculus BC test includes an Calc AB subset score (there's sections of the test that are like Calc AB questions, then they give you a grade for each) so if you just take the BC test you'll be fine. I'd recommend taking Calc AB just because unless you do lots of studying on your own, there's going to be a lot of ideas that you won't be familiar with, but will be assumed understood for BC.
Obviously the final choice is up to you, but I don't think pre-calculus is that amazing a class, it's honestly a lot like algebra 2/trig with a little bit of beginning calculus thrown in. If your teacher is willing to let you skip it and you like math, I'd take the opportunity, but my recommendation is you do take AB since BC is just repeating the same stuff (and then adding taylor series. That's the only thing that's new).