Eastern European countries have become popular in the eyes of backpackers in part due to the beautiful landscapes, but mainly due to the cheap prices they offer. A backpacking trip to Bulgaria is a wonderful experience.
The Bulgarian language is very similar to Russian, meaning Russian speakers will be able to speak and understand quite freely. Most of the signs are not in English, but you can get by with a good language translation app.
Bulgaria is a relatively safe country, but of course it is recommended to wear a money belt (especially on bus trips and crowded places).
In the big cities, you can find places in hostels relatively cheaply, and in the summer you can stay in a tent in designated camping sites.
In Bulgaria, there is a convenient bus network. In more remote places you might have to hitchhike. Trains are much slower than buses in Bulgaria and are not recommended.
The best time to travel Bulgarian mountains is between the end of May and the end of October. September is considered the driest month of the summer months and October is already starting to get very cold in the high places and most places are already at end-of-season prices.