Air Bagan is generally considered to be the most reliable airline in Myanmar. They have an extensive domestic network, including the routes you mention.
Purchasing tickets may be a little problematical. It is not possible to purchase tickets online, and you can't use credit cards in Myanmar. I had to use a Thai travel agency, based in Bangkok, who delivered the tickets to me at my hotel in Yangon.
Bagan is awesome, by the way. If the world (and, specifically, the Burmese regime) were different it would be one of the most famous and popular sights in the world.