It is perfectly possible to travel to Myanmar on a budget even if most travellers there tended towards the higher end.

Each town has hotels for local travellers, that are basic but much cheaper than the tourist oriented hotels but they are very basic. I think the last time I stayed in one about 18 months ago it was USD15 a night for an ensuite room with AC (but no TV no internet etc).

I would recommend Taunggyi the Capital of Shan state as somewhere to base yourself. There is plenty of hiking around the area, Inle lake is very close. It also has enough tourists so that there are a range of places to stay and tourist guides.