How does Bitcoin get over the capital controls problem?
Bitcoin is hard, but not impossible, to censor so if governments really wanted to censor bitcoin transactions they could do it. Right now governments seem more interested in wooing bitcoin related businesses to their countries because they see it as something that can contribute to economic growth. But, yes, if they changed their minds they could shut it down. 

However, what would happen if they shut it down? Would developers and users just give up? The answer is that we won't. We'll switch to crypto currencies that are even harder to shut down. Crypto currencies with anonymous ledgers like Monero. I don't think governments want that to happen. At least with bitcoin the ledger is transparent. 

There is a historical precedent to this. Bitcoin isn't the first attempt to make a digital currency. I suggest you read about digicash and the problems it encountered getting traction. If governments push people will push back!