Travel in Myanmar tends to be uncertain and uncomfortable. Many visitors are tempted to take internal flights because of the restricted 28-day stay regulation, but the poor safety record and 'flexible' notion of schedules of Myanmar Airways and, to a lesser extent, Air Mandalay, can be a deterrent.
Others opt to stick with transport not controlled by the government. The Yangon-Mandalay bus service is the most comfortable long-distance bus trip. Otherwise, visitors can pay a little extra to get a more spacious 'pick-up truck' that cram locals in the back and make many stops between towns all over Myanmar. Many visitors reckon train travel on Myanmar trains is like riding a horse - with saddle-soreness from hard-seat bouncing lasting for a day or two. There are daily express trains between Yangon and Mandalay; one service is run by a private company. Forget the ordinary-class trains, which are dirty, slow and unreliable.
Another alternative is arranging a car with driver; it's easiest to do with a travel agent in Yangon.
Getting around towns can be much of the fun. In most towns, including Mandalay, you'll see horse carts clip-clop by, and trishaws are everywhere. Once settled, it's usually easy to rent a bicycle for a couple dollars to join the fraccas. Always negotiate fares in advance.