Personally I find Estonia a far better option than Bulgaria because they have a 0% tax rate on retained profit within the entity so you can accumulate some tax free money there and the flat 20% tax on your withdrawals seems to be fair too.
Yes, nowadays banks tend to ask a lot of documents in general. Even 5 years ago it was completely different. I remember about two years ago I got a totally unexpected email followed by a call from Citi to explain certain transactions. A few weeks later I got the same request from Santander then from Standard Chartered. Why? I still don't know. All the transactions was from reputable brokers but they found it suspicious that I quickly forwarded the entire amount to another company so I had to explain that I had to quickly transfer the incoming funds because I wanted to exchange the money from one currency to another and your bank is expensive as hell. Needless to say I still haven't got a response.
Btw presently I think Malta is a good option if you're willing to travel around. If not then Estonia might be a good option. You can buy really nice and spacious apartments for $500k and the 0% tax still rocks.
Dubai... well, it's a touchy topic for me because it would be the best, I repeat myself, the best country on the world if religion wouldn't rule the place. Sunshine on 365 days a year, no tax, no compliance, no registry, no paperwork, no audit requirement, no filing requirement, 1st world city, looks amazing and highly developed, world class infrastructure and so on. The only problem is their religion. I can see that they're doing their best to be as tolerant as possible, I really see but it's just not enough.
For instance they could say that alcohol is legal in hotels and in a couple of bars and clubs. Why couldn't they say that non local citizens whose religion is not Islam, can have sex with whomever they want in their private apartment as long as they're not throwing huge parties and locals can't see it?! This law, this one law would turn Dubai into the best place on the whole world in a second.