Sarlat is truly a lovely place and yes of course you can take the bikes however the roads are hilly and often narrow and twisting so i guesss it depends on if you are experienced in this type of environment
Wayne - we stayed at les perrieres in Sarlat for two weeks this summer. Didn't take bikes and didn't miss them in anyway. Steep hills around the town and pretty busy roads between there and the lovely villages on the Dordogne. Unless it means an awful lot to you don't bother.
Carwyn