Nice to hear that ! So nice till u went twice? Can share me your itnerary and accomodations details and transportation etc ?
Yes, it is safe to travel alone but of cos u still need to be aware of the surrounding... I was there alone last yr and will be going again next week. Bagan is definitely a place not to be miss, 3d2n shd be gd enough. Inle Lake and Mandalay are also the top destination for most traveller. They have domestic flight and bus (JJexpress etc) to travel around the country.
Overall it is possible to do FnE, a lot of guesthouse available. Accommodation is not cheap in Myanmar if u would to compare with other region in SEA.
For how many days is required... depends on where u wanna go but my recommend is more than a week. Cos u do not wanna spend $45 on the visa for short trip.
Hope I have answered your questions. Feel free to ask more.