I need to make a semester project for my AI class at school, and I'd love to make something with a little more interactivity than algorithms and CS theory. I want to see if I can make a rudimentary drum accompanimant in Processing.

Please throw your two cents in and help with the brainstorming! Its going to be using my computer mic input, and I hope to be able to play some chords on my guitar in a rythm, then have the program just hit a bass note or something to it.

Whats a good way to get a really, really simple real time drumming system working in processing?

Not to prevent you from using processing, but there are other programming environments which will make it much easier for you to code real-time audio. You should take a look at ChucK, which is linked under related initiatives on the main page. They have some good demos, including how to get microphone input into your "shred" (equivalent to a processing sketch). Good luck with your project.