Question about RN

There is no such thing as an RN degree. There used to be RN diploma programs however, they are being phased out. You either enroll in an ADN (associate) or BSN (bachelor) degree program. Some schools also offer entry level nursing MSN (masters) program. Have you researched schools? What program do they offer? An ADN or BSN?

You'll only have a BSN if you are going into a BSN program (or a program where you get a BSN on the way to a masters). Your first degree doesn't matter beyond you already having maybe some gen ed classes and such.

And you can become a Nurse Anesthetist after some years of experience and then getting the right masters program and passing an exam.

No it will not be the same. A BSN is a bachelor of science in nursing. You will have a Bachelor of Arts in Biology, and a second degree (I'm assuming associate degree?) in nursing. This second degree will allow you to sit the NCLEX for liscensure as a Registered Nurse. If the nursing program you are going to is an associates level nursing program there are many programs that allow you to bridge to the BSN degree - and this can be a great way to get your BSN as these programs assume you are working as a nurse, and some employers may help with tuition for finishing out the BSN.

I know there are programs that allow ADN/RN to bridge to MSN with out a BSN if a person has a bachelor's degree in another field, but I am unsure if any of these set you up to transition to the CRNA role. You'll have to investigate CRNA programs and see what their admission requirements are.

You will have a BSN if and only if you attend a BSN program. BS or BA + ADN does not equal BSN.

If you want to become a nurse anesthetist, you do that by attending a CRNA program. Being an RN (with critical care experience) is generally a prerequisite to these programs.