I say this owning a very shy dog who barks and growls (not ferociously, but enough to startle people) sometimes at people who approach her, and especially would have in Mia's situation. I still take her out, because 99% of the time, it's not a problem. I ask people to leave her alone, I block her if I need to (I just had to do that yesterday at a park when a child ran up to her, arms waiving, yelling "puppy, puppy, puppy!"), and I give people very obvious body language myself that you do not come near my dog if they ignored the first polite warnings I've given them already. Dance has never bitten or attempted to, but still. I know certain situations make her severely uncomfortable, and so I do my best to make sure she doesn't have to experience those. But at the same time, despite not enjoying strangers at all, she DOES like to go out and do things and is quite happy just to focus on me and our time and normally everything goes nicely. There was a point in time that (when she was more reactive than she is now) I felt similarly to you. If there was a bad situation, and Dance reacted, I immediately went into "well, now I guess we can't go there anymore" mode and was super upset about it.
I guess it all depends on the situation and the dog too though. So definitely do what you are most comfortable with. I just know that in my experience, Dance and I would have missed out on a lot of really great days if I let a bunch of bad/embarrassing experiences get to me too much. There are absolutely certain situations that I do avoid with her both for her sake and for mine, but compared to my thought process of being doomed when I first noticed all of her many, many issues, we actually go and do a lot of things and have a good time and I find I don't need to avoid many of the places/things I thought I should upon more thinking and a game plan.