If you're willing to go to North Carolina, Humane Alliance was one of the best spay/neuter experiences I've ever done! It cut my spay time down like crazy (I was down to 12 minute cat spays when I left) and I did about 30 surgeries while I was there. I also was just so much more comfortable with surgery in general after that externship. If housing is your concern, they also offer dorm style housing with the other vet students at a fairly cheap price on site (I think it was like $50 a week or so?).
Aside from that, I don't know of any specific places in Virginia/Maryland. A quick google search gave me the VMRCVM list of shelter externships, which has some that are located in Virginia/Maryland. (Link here:
Humane Society / Rescue League Clerkships and Externships) They don't all look like they are specifically spay/neuter, but you can still get a decent amount of surgery experience on shelter medicine externships (just expect to do some medicine too). You can also just contact them and ask about specifically arranging a surgical externship to see if they would adjust their clerkship to suit your needs.
Once you do get a little more comfortable with surgery, if you want to get more experience I'd recommend just emailing around to any local shelters in your area. Tell them your level of surgical experience and that you have some free time and would like to help out in surgery if possible. I did that after Humane Alliance, and one of the shelters in my town has an extra surgical table so they've let me come in whenever I was available over the last couple months. I've done about 110 spays and 150 neuters in the time I've spent there. The only downside is that their spay/neuter vet is always super busy so I didn't really get any training/instruction after she watched me do the first few spays. Of course she's there if I ever run into problems, but she pretty much leaves me to my own devices since she has so much to do herself. So unless you know they'll be able to provide you with more attention, I would definitely recommend doing an externship first to get comfortable spaying/neutering on your own!
