There is a boat from Mandalay to Bagan that many tourists and tour groups use, its a nice journey but.......there is a boat from Bhamo that is used 99% by locals.You may be told that foreigners are not allwed on this boat, but its not true. Its slower and as a foreigner you are required to buy a cabin, I think it was $20 and it includes 2 hard beds and running water (for a while), no private toilet, you must share with the "first class" passengers. The two day journey is beautiful, thick vegetation along the river, stopping a small villages along the way. As the only foreigners onboard, at first we were a bit of a novelty, attracting stares and pointed fingers, but the two days allows you to become familiar, not to mention endless photo opportunities. The boat does not go all the way to Bagan, you have to get off a little way up river and either get another small boat or pick-up. Both of which were easy to arrange.
Enjoy Burma at its best!