What qualifies as a BSRN?

You'd be an ADN with a BS in bio. You need to complete the additional nursing classes in the BSN program to be considered BSN.

Nursing education is done via "programs" rather than a series of classes that are interchangeable between schools. All accredited programs have to include the same basic content, but they may choose to do it in radically different ways & may include a lot of extra material as well.

In addition, In the US, there is no "R" in a nursing degree because the R means "Registered" and this only comes when you have passed your licensure examination (NCLEX) and this process is managed by each state's Board of Nursing - not by schools. So we list our educational and licensure credentials separately - "BSN, RN or ADN, RN" But don't worry, you will be able to find many "bridge" RN to BSN programs designed to meet your needs.

I'm a bit curious about what exactly qualifies as a BSRN. After this spring semester I'll be graduating with a bachelors in biology with a pre-med minor and in spring of 2014 I'll also have an associates degree in nursing. With the bachelors in biology, would my associates in nursing be looked at as a BSRN, or would I still need to finish a BSRN completion program?

You will be an RN with an ADN. You will not be qualified for any nursing job that requires a BSN. When looking at job opening that says "BSN required" you will not be qualifed to apply. When you get a job and some experience and want to apply to managment jobs that require a BSN you will not be qualifed.

In nursing this is realiety:

BSN = BSN

ADN + any other degree = ADN

According the the dean of our local community college ADN program between 1/3 & 1/2 of their ADN students already have a bachelors or higher degree in other fields. I often wonder why people with degrees in sciences bother with nursing school but a lot of them do.

If I were you I would forget the BSN (that's what it's called, not BSRN) and go strait for MSN once you find a job.