This is my perspective, and maybe it will help give you the courage to ask. There is a shortage of NPs, and while the schools try to graduate more students, there will be more students than preceptors. However, if the NPs who are working don't precept, then there will be no new NPs and they will be even more overworked. As nurses, we are all used to having to teach the next generation. It is just part of being a nurse. Precepting a student makes the preceptor stay up-to-date on information and keeps them in touch in what the current students are being taught by their schools. Plus as you get further along in your clinical semesters, you will be able to help with their work-load, by doing some of the work and they can just review and sign off on it. It is not like an RN program. You should start with a pretty good idea of what you need to be doing. It varies somewhat on settings, but for my primary care hours, I was going in and doing all of the initial questions and exam on my second day of clinical. Then I reported to my preceptor when I learned and found and she would go in and just confirm that I didn't miss anything and put a plan together. I have never felt like a burden to my preceptor. You don't need to compensate them for their time. Just make sure you're a good, prepared, interested student. There are very few nurses who don't like teaching (the profession is a bad fit if you hate teaching, lol), so just be the type of student that is fun to teach
Good luck in your search. I had to find all of my preceptors for my program and this worked out great for me. The only time I had trouble was for primary care. But I loved the flexibility to work with the people that I thought could teach me the most. It isn't all bad finding your own preceptors.