There are some Bachelors to RN programs out there. Do a google seach. There are also some BA to MSN programs that don't require nursing experience like this one Pre-Specialty Entry | Master of Science in Nursing | Vanderbilt University School of Nursing
I am not sure about financial aid but usually if you already have a bachelors it is hard to get aid for another bachelors unless you are going for teaching.
I did a post bac program after my BSN and had to pay out of my own pocket for everything. If I had done a Masters it would have been covered by financial aid. So it might be better to try to go the Bachelors to MSN route but you will have to talk to the financial adviser at the school to see exactly what the financial aid would cover.
You may have to do some health science related pre reqs for these programs but would be a huge shortcut for you since the ADN is also going to have pre reqs. The trend for hospitals hiring now days is to hire nurses that at least have a BSN because they want to keep or get magnet status. They are even making ADN employees go back for their BSN to keep their jobs etc.
I really think you will have a broader range of possibilities with nursing than respiratory but totally up to you. They are both worthy professions. See if you can shadow someone and see what they are both like.
Another idea...if you haven't finished your bachelors maybe once you figure out what Bachelors to MSN program etc that you want to do, if possible, try and squeeze in some of those science pre reqs in. That way they will be paid for with the first bachelors.