Agree totally with all the above. Don't worry about bugging them or them not remembering you.
Do make it as easy as possible for them.
-give them addressed and stamped envelopes
-give them deadlines
-tell them which program/area of interest so they can write a better letter
-go by for their office hours so they can ask you questions/chat
Some professors have a form letter and just fill in your details. Other (good professors) write specific letter for each person.
Good luck
@WasabiPoptart!