You do not need to become a RN first before getting your BSN. I am an RN who entered the field with a BSN without first getting an ADN. (Not that there is anything wrong with ADN programs- I do not want to get into that debate here- this is just the path that I chose for myself).
There are 2 ways to become an RN. You can either get an associate degree in nursing or a bachelor's degree in nursing. Look at universities in your area for nursing programs. You will find that there are BSN programs which do not require an RN license to be admitted. There are, however, BSN programs out there that are designed for RN's with associate degrees, but this is not what you are looking for. I hope that I have helped to clear this up for you a bit.