I feel like I'm in a similar situation, and its beginning to weigh on me more and more as I realize I need to ask for letters in the near future in order to have them done in time for next summer.
I'm a good student - I work hard, do well, attend class, participate when appropriate, etc. But I've never been comfortable buddy-buddying up with my professors by taking up their time outside of class. Maybe 2-3 times per semester I'll have a legitimate question or otherwise valid reason to visit them during office hours, but I would feel like a big fat obnoxious brown-noser making it a weekly thing when I would obviously only be doing so to try and "show off" and impress them so I can ask for a LOR later on. Nearly all the profs I've ever had are very busy and would see right through that and most likely be annoyed after a while. I feel like I'm much more professional and respectful to them by going the extra-mile academically (high grades, excellent writing, etc.), but other than that being as "low-maintenance" a student as possible.
Shouldn't that be enough to ask for a good LOR? I've heard people say "Just doing well in a class isn't sufficient merit for a strong LOR" - but what more, really, is a professor whose class you've taken qualified to evaluate you on other than your academic performance? You have a PI/employer to write about your work ethic/professionalism/extra-curricular intellectual pursuits and a letter from someone more personal (like a volunteer director/mentor) to write about compassion/altruism/interpersonal skills. I know I need to ask for some LORs soon, but I'm nervous about how to do it and if my performance as described above will be enough to get me good letters from the professors I have in mind.
I, too, would greatly appreciate any advice from people who have been through the process already and can maybe relate a little bit to me and the OP.