Need some advice

I am trying to find my clinical placement, but I wasn't born and raised in Florida. My college leaves it up to the students to secure clinical placement, luckily I can do 90 hours at my hospital with the nurse practitioner I know, but after that I need to still fill over 500 hours! I'm very stressed cause I don't even know how to go about finding someone to help me. My primary care provider is a DO and she suggested I look up practitioners that work for her practices health system. I certainly don't want to book an office appointment and pay a copay to ask a stranger to precept me, I feel like it would be rude and putting them on the spot. I was thinking of drafting up a letter to deliver to the office addressed to the NP and explain my situation, and stating if they are interested in precepting, requesting we meet outside of office hours to discuss my educational needs. But I also am not sure how well this would be received. Any tips or tricks?