I was in the same boat, as I finished my bachelor's degree in 2004 and had difficulty finding science professors who still remembered me (although it helped that I was one of those students who asked a lot of questions in class). I am fortunate to be accepted to med school this year, so I will share my suggestions.
First of all, find out if all schools require 2 science letters. Most require at least 1, and there are very few schools that simply require you to get a letter from academic or work-related individuals who know you best.
For schools that require 2 letters, ask to see if other semi-science related subjects like biostats or math or engineering professor letters can be used. Some schools may possibly allow you to do this if you explain your situation to them and get permission.
I emailed a bunch of my old professors, but few still remembered me after all these years. Although it was awkward writing letters to professors years later asking for assistance, I explained my situation about how I was in a pinch trying to find letter writers after all these years. In science classes where I had an 'A', I defintely mentioned that in my email to that professor. One initially agreed to meet with me, but later declined- saying she didn't remember me sufficiently and could only write a very generic letter. So that was unfortunately a no go. (I still would have used her letter if I had no other options, but fortunately things worked out for me... continue reading below...)
I ended up getting a letter from an organic chemistry professor who had me for 2 years. (I got 'C's in orgo 1 & 2 the first time around, and then repeated both classes the following year and did much better.) Taking a letter from him was a huge risk, as he is a stoic person and I had no idea what he thought of me, or if he liked me at all - especially as I got 'C's the first time in his class. I took my chances though (since I was desperate), which luckily worked out - I suppose at the very least he could say I was persistent enough to not give up and take classes with him again (as he was the most difficult ochem professor) until I succeeded.
For the second letter, I just couldn't find another science professor to write me a letter (as my graduate coursework was all non-science. I had no trouble at all getting non-science letters, as my graduate and work-related supervisors wrote those for me gladly. But finding science letters was super difficult. Most of the professors I wrote to either ignored my email or declined my request. Rejection... ouch.). I had one physics TA who agreed to write me a letter back in 2004 (as I was considering going to med school back then), so I thought I'd take a chance to see if I could still find him over the internet and see if he might still remember me enough to write a letter. Unfortunately I couldn't locate him online. I remembered another science TA (in an upperdivision class in which I received a 'B' in 2003) who I had met with many times for tutoring. Thankfully I was able to reach her online, and she finally agreed to write me a letter. The professor whose class she TA-ed for only remembered me vaguely (which is lucky at all, due to my always asking questions in class). I remember when I took the class in 2003, he told students that he would only write LORs for students who got 'A's in the class, not 'B's. So I did not bother to ask him directly for a letter, but when I told him that one of his former TAs was writing me a letter, he agreed to co-sign a letter if the TA would write it - which she did. Phew....
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So after all that stress of finding science professors from 2003-2004 classes, I was really lucky to get my 2 letters at all. It was REALLY difficult finding people and almost kinda embarrasing to ask people for letters 4-5 years later from when I took their classes. But I had to swallow my pride to get things taken care of. I also took a lot of risks asking professors in whose classes I didn't have 'A's in, but in my case, my selection was limited... as I was lucky at all to find people who still remembered me enough to write letters. I was also fortunate that my non-science professors/supervisors adored me, so in the case that my science letters were not as strong, at least my other letters may have made up for it somewhat.
If you absolutely cannot find people to write you letters, the only other solution is to take a few spring/summer science courses and ace them and hope 1-2 of your professors will be willing to write a letter. While I ended up being lucky that my letters were good enough to get me accepted, but other students may not be willing to take that risk. In that case, it may be better to get 'A's and find teachers who you feel confident really like you, rather than being forced to ask widely in hopes someone still remembers you from years prior.
Hopefully my experiences may be helpful to some of you. Although asking widely for letters wasn't fun, now that I have been accepted to med school... it was definitely worth it! Good luck!!
