The Forest of Bowland is famous for cycling and there are lots of great routes. If you google cycling in Bowland or in the Ribble valley you will find lots of suggestions. Or you can you just hit the road and see where you end up – you can hardly go wrong (as long as you have a map with you so you can find your way back!)
My favourite ride is a circular ride via Newton, Dunsop Bridge and Whitewell. Turn left out of the Old Forge and cycle along the road as far as Cow Ark, where you turn right towards Whitewell. Soon after, turn right again onto the back road to Newton. Eventually, this will take you to the main Clitheroe-Newton road, where you turn left and cycle down the hill into Newton (perhaps for some quick refreshment at the Parkers Arms). In Newton, turn left onto the winding road to Dunsop Bridge. Carry on through the village and out on the same road, which will eventually bring you to Whitewell. If you’re feeling energetic, you can turn left in Whitewell to take the fell road back to Cow Ark – the shortest route and very beautiful, but steep. If you’d rather take it easy, carry on the same road through Whitewell and then turn left over the river back to Cow Ark.
If you want to do a shorter circuit, don't turn right to Newton when coming out of Cow Ark but continue on the Whitewell road. This will take you Whitewell over the fell, and you can then come back the lower route as described above.
The most famous ride is through the Trough of Bowland. To get to the trough, cycle to Whitewell as above and then on to Dunsop Bridge (or for a longer route, go via Newton). As you are coming into Dunsop Bridge from Whitewell, the main road bends sharply right and a smaller road continues straight on – this is the road to the trough. If you continue on the same road, you will eventually end up in Lancaster (it’s around 18 miles of hilly road from Bashall to Lancaster). You can get the train back to Clitheroe from Lancaster with your bike if you don’t want to do the return cycle (this involves changing trains in Preston and Blackburn).