There is not that much equipment that is critical for this trip - just the camping basics, really. Some people (poor Co-ops) like go cheap-and-light. Others (professional engineers) like to travel with fancy, high-tech gear. This trip is a great time to try out experimental camping gear arrangements, if you are so inclined.
Things each person will need (I suggest):
-Bike (mountain or hybrid, not road bike... also, it can be cheap and crappy - my bike cost $120 at Walmart 6 years ago... note that bikes can also be rented pretty easily around here)
-Panniers / storage for your stuff (you can buy/borrow panniers, a trailer, or just put your stuff into bags that you bungee onto your rack - there are many options that will work depending on how fancy you want to get)
-Food (snacks and a few meals, and more if you don't want to do restaurants)
-Tent (or space in someone else's)
-Proper clothes (probably 2 sets of clothes, plus rain and cold gear - this is plenty. You can get "high tech" clothes or just wear old tshirts)
Inner Tube - in case you need it - chances are someone will have a flat
Things you probably want to take (or ensure that someone takes for you):
-Headlight/tailight (in case of night riding)
-sunblock/bug repellent (I don't use it, but I take it anyway)
-personal hygiene stuff
-TP (not everyone needs a whole roll, but you don't want to run out either)
Other things to maybe take:
-pad and pen
-"blue" polyethylene tarp
I will be taking a whole bunch of bike maintenance stuff, but everyone should make sure that they have at least 1 inner tube for their bike.
The costs for the trip depend mostly on how fancy you want to get with the equipment. Bike rental is probably about $30 a day (this is a guess) or you can straight up buy a passable bike at Walmart/Target for $125 (make sure it has mounting holes to mount a rack). Buying a bike rack (needed for most people) will cost you about $30. Transportation back to DC will probably be about $85 a person. Campsites are free, and the remaining costs depend on you - you guys already know how much a meal in a restaurant costs if you want to go that way (I highly suggest restaurants), and the equipment above ranges greatly in cost from nothing (if you borrow it or already have it) to big bucks.