Do I need a folding bike to do this? What are the rules? Also, even if it's allowed, is it practical to do so? Subways get pretty crowded during rush-hour, and it's hard to imagine taking a bike there even if it's allowed.
Bicycles are allowed on the subways at all times, but the MTA suggests against taking your bike on the subway during rush hour.
Bicycles are permitted on Subway trains at all times. However, we strongly recommend that cyclists avoid boarding crowded rush hour trains.
Folding bicycles are permitted on all trains and busses except for express busses. Once folded, a bicycle is really no larger than most other luggage.
When taking bicycles on the train, be courteous and use common sense. Don't bring a bicycle into a car that's too crowded. Let people out before getting in. Don't block the doors, keep control of your bike so it doesn't roll into anyone when the train starts or stops, and be aware of when people need to get by. I only ever take my bike on a train if there's enough room for everyone to sit; if it's crowded enough that people have to stand, it might be getting too crowded for a bike.
According to the MTA, bikes can go on trains, only folding bikes can go on buses.
NYC Transit Subway
Bicycles are permitted on Subway trains at all times. However, we strongly recommend that cyclists avoid boarding crowded rush hour trains. Be courteous to your fellow passengers by standing with your bike, moving it so others can pass, and not blocking doors. Read all about Subway bike safety and courtesy.
NYC Transit Bus and MTA Bus
Folding bicycles are permitted aboard local and limited buses at all times. Please fold your bike before boarding and don’t block the aisle or doors. Folding bikes are not allowed on express buses. All other bicycles are prohibited.