OK, OP. It sounds like you're assuming that's the only reason a woman would go to a bar alone?
I'm 49. I do go to bars on my own. Well pubs anyway. Usually, only if I already know the place but I have been known to go to other pubs on my own. I'd never go with the intention of meeting someone though. It's usually because there's a band I'd like to see, i like the environment, I'm at a loose end or because I know they have a good selection of ales on.
I don't appreciate being 'chatted up' and give pretty short shrift to anyone who is clearly doing that! Especially if they'd assumed that was the reason I was there - it never is.
But I am open to having conversations with people. If a man approaches me and starts a conversation, I'll engage until I don't want to anymore. Sometimes, conversations will last a couple of minutes and sometimes, if we click, I'll chat for longer.
If a man, under those circumstances, asked for my number and said he'd enjoyed talking to me and would like to see me again, I might consider it (were I single, which I'm not).
I've been going to pubs on my own for a fair few years so I'm pretty good at spotting men who are out and just chatting vs those who are on the prowl.