Yep, This region has so many bike paths that most commuters can ride to one of them pretty quickly and make use it for the bulk of the commute. As for access to this Area B, see map below.
There is a bike path running parallel to Springfield street, the road on which is Gate 1B. This path connects to the Greene County trail system to the East and the Dayton system to the West. Nice areas to live exist along both trail systems, but I prefer Greene County for a number of reasons.