Yes bicycles are available for rent in Manali. Thrillophia offers cycle for rent. They have two kind of cycles for tourists. Their pick and drop location is at Manu temple. Thought of sharing a Tripoto link written by a traveller about his cycle expedition in Manali see if it is suitable for your travel. https://www.tripoto.com/manali/trips/cycling-56a9dade7d4ac