I get all

at first as well. But with time, just thinking about it for some time, getting used to the thought, seems to help. And getting things on my terms helps as well. Going to a place I know for instance, is a lot easier than going someplace unfamiliar. Or if I can scout out the place in advance
Knowing who's coming as well, is something I need to feel safe enough. If it's just the two of you, though, that's not an issue - then I would have to overcome the one-on-one issue instead.
If it's a restaurant, knowing the menu, knowing where the toilet is, reserving a specific table in some corner (not risking having to sit in the middle of the floor with tables and strangers all around), all helps me feel safer. The more I know, the less I need to worry about in advance.
I don't know if you feel the same, but it might be worth a try