Could you switch to a different bar not to be recognized as such?

Yup, one can do that. And then build up a mental map, of places to avoid, leading to embarrassing situations later on ...

What worked for me, was travelling. It is easier to relax, thinking, you will likely never see anyone here again.

(even though the world is quite small and I did in fact saw many again, but that was cool)

Another thing that can be much easier while traveling if you have anxiety is dating. Like you said, there's the comfort in knowing that you'll never see any people there again if you so choose. But if there's also a language barrier, it removes any expectations of witty banter and flirtation that usually relies on familiarity with your local culture and social norms. And there's less pressure to be interesting -- just being a foreigner will often make you interesting to locals without even trying, at least a first.