Hi Karolinka!
Very short reply on the yoga studios in Sofia: there are fat burning yoga classes in Maleeva tennis club, which resemble more yoga style gymnastics; you can find out more about it on their web-site http://maleevaclub.com/en/groups.html, in English ;).
Another place is Spartak sports complex, classes are led by Prakash.
The third one I could think of is Yoga 37; what is specific about it is that the classes are held at room temperature 37 Celsius; site is www.37yoga.com.
Personally I used to visit the first one and was quite content with it. Time start again, although I can't seem to find the inner strenght ... ;)
Good luck!