One of my local bike shops, who specialises in vintage and in used clunkers, services the student community.
Every Sept he sells a few hundred used bikes to students, and buys them back in July, then services them.
Most cost £50-100 which is well within the grasp of any student.

Bikes are so cheap, and the alternatives so expensive that schemes to make them even cheaper seem crazy. Free bikes are valued as much as they cost, and most end up discarded. Some free bike schemes make their bikes unstealable by making them really bad, with 3" wide solid tyres