Mobility is an important part of local access and I looked at a number of related library programs -- some that make transit access a part of library membership, some others that work with communities on "Safe Routes" programs.
Here's a project in Boise, ID, partnered with Safe Routes there, this year giving refurbished bikes to 320 kids. No library involvement that I'm aware of. But as libraries have looked for ways to support biking, this seems promising. Could also imagine it having a circulating aspect: "take a free kids bike, please return it to the program when you outgrow it". It's a big undertaking, but consistent with librarians' skills organizing partners and working with volunteers.