Could I possibly go to a college and get my Bachelor's degree in Biology, and transfer to a different college to get my Master's in Marine Biology?

I don't see why not. Obviously you'd have to find a school that offers a Master's program in Marine Biology.

Yes. Your undergraduate major does not determine what you get your graduate degree in. You could get a BA in math and then get a Masters in Marine Biology provided the particular grad program accepted you. (They might make you take some catch up courses.) Biology is fine preparation for marine biology.