With a BS degree why are you looking to enlist? You should be talking to one of the officer recruiters. Unless of course, you've done that research and just decided enlisted is what you want to do....
I also have Bachelors of Science degree and I am enlisting. I didn't have the calculus and the calculus based physics.
That is why I didn't go officer. That may not be your reason, but I know what you are going through if it is, and I know several enlisted soldiers and sailors with degrees.
I heard of this loan repayment program that the Navy offers. Would I qualify for both the enlistment bonus and the loan repayment program?
I say that to let you know my background. The way it was explained to me about the bonus versus the loan repayment, for starters, is that they will only repay your government loans. This means that if you have a lone from a bank, they will not pay it. They will have what federal loans you do have when they look you up on their computer. Mine were two federal perkins loans as an example.
For me, my bonus was greater than the loans that I had, so I took the bonus over the loan repayment. You cannot have both of them. You do get the choice as to which one to take and it is pretty easy to pick the best when they are laid out in front of you. My bonus was $10,000 more than my loans, so it was a no-brainer.
Hope that helps.