Opposite to what most of the local travel agents and MTT office state: it is possible to go by bus from Bagan to Mrauk U directly without going south to Pyay. The bus trip takes about 20h (more depending on the connexion in Magwe).
From Nyaung U, take a local bus to Magwe (4h). There are many buses during the day, you might need to ask a local agent (the guy at Morning Star on the main road was very helpfull) or your gesthouse to help you catching the right bus on the road since they are not stopping at the bus station. In Magwe, you can catch the direct bus Mandalay-Sittwe at around midnight opposite of the Rolex Guest House to which you need to take a taxi from the local bus station. The direct bus requires you to pay the full fare price Ky 25'000 + an additional Ky 5'000 supplement for foreigner. The ticket can be brought in Magwe at K.M.H Fashion Shop, tel 095680758 opposite of the Rolex Guest House, the shop owner Minn is very helpful and speaks well english. The bus ride from Magwe to Mrauk U takes about 14h. There is one police check on the way which asks for copies of passport and visa (since I did not had one, and they just wrote down my passeport number in a book).
In the opposite direction the same trip is possible as a french couple reported to me.