Oxford’s cycle routes form a dual network. The main routes follow normal traffic corridors. There are quite a lot of cycle lanes, traffic is not too bad, the junctions are OK, but take care around buses. The quiet routes avoid the traffic (mostly). They aren’t always well-signposted, but you can see them on OpenStreetMap, or on Cyclox’s own map.
Using the same data, this Journey Planner, will work out a route for you.

Printed copies of the County Council cycle map are also available, though it’s a little out of date, and not as clear. The County Council bus map and central bus stop guide are much more up to date.