There are many connections from Manadalay to Bagan. It is a 6 hours drive and goes quite frequently. We booked our bus ticket through our hotel. It ended up being quite a long 6 hours ride as it was a minibus that was very uncomfortable.
We were dropped off in a town just outside of old Bagan from where we had to take a taxi. Try to share a taxi with other tourists to minimize the costs. Travellers usually stay at Old Bagan or Nyaung U.