Many cities in Europe already have bike sharing programs in place. Some cities (like Paris) offer free bikes funded via advertising and others are paid for with taxpayer money (London). These programs offer many of these sturdy, “granny type” bikes with baskets and many stations installed in former parking spots. Unappealing as they sound, they are more a tool for transportation and curb the idea of stealing.
The US is finally offering this type of program such as the one Washington DC: the SmartBike DC Program. This is a fully automated touch-and-go rental program with 120 bicycles at 10 locations throughout the city center, supported by Clear Channel Outdoor and the District Dept of Transportation. Subscribers will receive a personalized SmartBike DC user card that provides access to any station of the program at any time.
Maybe your city will offer this type of service soon and the library can be a part of it by supporting the idea and offering a station outside the library building!