Getting around Myanmar can be done by plane, train, bus or river boat. Several trains a day travel between Yangon, Mandalay and further north, with both government and private operators. Most trains are overnight, as is the bus service. Seat 61 has, as usual, some great, current, information about getting around by train.
If you have plenty of time, the river is an interesting option for travel from Bagan to Mandalay (or vice-versa). Both 'slow' and 'fast' boats are available, although the fast option may still take a full day of travel.
Airlines Serving Myanmar
Several local "private" airlines now serve Myanmar. Some of them are to be avoided. Listed here are the best candidates to consider.