There is no really bias against non-trads from what I have seen. However, saying you are pre-med and wanting to work in a basic science lab might be different. They tend to have a preference for people who are aiming for a masters or PhD. I kind of felt this bias when I was trying to find a lab to do research in. As for clinical labs, I am uncertain and wish I could have worked or even volunteered in one.
I think the main thing is to have something you are really interested in. If you really show a interest in the research area that the PI of the lab has (does not have to be the exact same thing but close), then it really helps in getting a position. It is possible to be a volunteer researcher but sometimes this can be difficult too. I am currently doing a research rotation but only for a semester because the PI cannot take anymore students.
Sorry if I sound negative on my post but it is still possible to find a PI do research under. However, you could be emailing up to 30 professors just to get into one position but once you are able to get into a lab it is worth it! I definitely gained a lot of knowledge from the neuroscience research I was doing and am glad to be here even for just a semester.
Main thing is just be persistent and it will pay off. Trust me.