A couple years ago I applied for the MSC IPP Rad Health Officer program. If you read OPNAV 1420.1A (I'm pretty sure that's the current rev) you'll find that you do NOT need a BS to start the program (they have a completion program for this). I talked with quite a few current RHO's (and met a few former ones last year too). Most of them went through a recruiter to get into the program, however.
If you want to get a good insight on what RHO's actually do on and off the ship (its not really THAT self explanatory), read some of their instructions (P-5055 comes to mind). Talk with the dosimetry guys (not just any ELT, the ones that actually work in dosimetry, the dose sup would be best) on your ship to find out their interactions with the RHO on a daily basis (Oh yeah, RHO's have to qualify TLD Reader too).
As an RHO you will need to be eligible for a TLD for shipboard duties, but the requirements for issuing TLD's to sailors outside the NNPP (RHO's do exist outside the NNPP thats why they are part of medical Dept.) are different, so you still might qualify (talk to your current RHO about this).
NKO has a radiation health officer community page which gives some really good info on the community (also you can find more than one RHO to give you an interview this way). Look under the medical service corps communities to find it.
CAUTION! SHAMELESS PLUG AHEAD!
For some more info on the wonderful world of radiation health, I would start off with the health physics society website,
www.hps.org . It may not be Navy specific but it is really good to get an idea of the career field you are choosing by going into RHO.
Good luck,
Jason