As stated above, there is no formal "Paramedic to BSN" program. That being said, if you took courses at a community college or university, you may be able to apply those to completing your BSN program prerequisites. Since you already apparently have a Bachelors, you may be able to get into an accelerated BSN program, which is basically the Upper Division BSN program without all the "extra" UDGE that you'd normally take when doing a BSN as a first Bachelors. ABSN programs also usually run straight through, so if it's a 4 semester program and you start in the Fall, it goes: Fall, Spring, Summer, Fall.
I did a traditional ADN program and I have a Sports Med Bachelors. Most of my prereqs for that were also prereqs for my ADN program (and also for BSN and ABSN programs, but none were open to 2nd Bachelors students at the time). I'm also a Paramedic. My Sports Med education was far more rigorous than either Paramedic OR the RN programs that I attended.
The NCLEX doesn't accredit any program. It's only an exam. What you're looking for is a program that is accredited (at the minimum) by your state's Registered Nursing Board as providing the education necessary for initial licensure. If the program is also ACEN accredited (they accredit Masters, Bachelors, Associates programs) or CCNE (they accredit Bachelors and above only), then that may be a bonus, but the program must be BON/BRN approved for it to make you eligible to take the NCEX upon successful completion of the program and ACEN/CCNE accreditation is not usually a BRN/BON requirement for their approval.