Congrats on almost being done with your PhD. I'm 29 and live in the DC area.
Great. I only asked your age because we had a 65 year old man come in last year hoping to volunteer and get his hands wet before applying to graduate school. My advisor is an extremely liberal/progressive/open-minded woman, but even she had her limits and had to give the guy a wake-up call... It seems like you'd have good access to research labs (Hopkins/NIH or even Gtown).
The most important part of biology graduate school admission is research experience. Everything else being kosher (GPA>3.0, good personal statement, etc) traditional PhD students coming right out of college generally can be successful with 2-3 summers' worth of full time research (think 9 months total). Usually these are in different labs or internships in industry, so they get several recommendations from different PIs/group leaders. The lore is that if you can get a PI at a research university to say that they would personally advise you in their lab, you can get into that school.
It's a very fluid process when you compare it to medical school admissions, which in many respects can be extremely rigid. While medical school admissions tries to see if you'll be able to survive the mountain of coursework and exams in the coming decade, graduate schools want to assess you for the potential to stick to a very grueling project to at least finish a 6-year PhD. You should be able to demonstrate a wide range of research techniques and experience in different lab environments, presentation/writing/talking skills (aka being able to describe your projects with passion and comprehension), and very importantly: an intimate knowledge of experimental/project failure and how to overcome it without giving up.
As for biology classes, I would recommend "taking" any coursework you deem relevant just so you have the necessary basic background to understand the research going on in any labs you'll be working in (just audit classes for free - there are no formal pre-reqs for PhD programs, and we have CS/engineering majors doing Biology PhDs all the time). You can also use MIT's opencourseware to listen to lectures for free:
http://ocw.mit.edu/index.htm
This is the long route - take it if you're looking to get away from what you're currently doing and move toward wet benchwork: Seek out labs who will take you as a volunteer. I would aim high in terms of caliber of school/lab. The research university is (unfortunately) an ivory tower, and once you're in (in any way) it's easier to stay in. Send out emails to groups whose research you are most passionate about/interested in. I'd be happy to proof your emails if you PM me. Ask to volunteer to do the most menial tasks (making media, petri dishes, restocking, etc). When you are in a lab, go to seminars, lab meetings, and form a relationship with your PI. Eventually you can work toward getting hired as a technician (in this lab or another lab), and usually with 1 year of solid technician work OR volunteering on a specific project, you'll be good to go in terms of credentials.
The shorter route to this is to simply take the GRE and apply to graduate school. This may possibly work if you have research experience in other fields. Explain your interest in biology (especially connecting it to your own current expertise), and meet with group leaders who would find your skills valuable. Many graduate students are coming from totally different fields and are very successful learning biology on the job.
.
