If someone says "You're welcome any time" how do you visit "any time" without a specific invitation, without it being like you're inviting yourself?

I would call up and say, you said “any time” so when would you like to get together?

It’s just a shallow saying, like “How’s it goin?” No one actually wants to hear what you have to say lol. You should always make plans with someone.

People say that and not really mean it. As in don’t show up the next day but more like next month maybe or longer.

When I say that line to people, I mean it.
Because I really mean it I don’t say it often, but when I do I (may) expect to find that person on my doorstep any possible moment.
If someone says it, I think they should not be surprised that someone keeps them to that invitation.

They are usually full of baloney.
When you’d like to get together with them,call!

You could always call and say “I’m in the neighborhood… want to have some coffee?”

To me that means to feel welcome to ask them to get together sometime.

I don’t think it means you’re welcome to come without notice. I think it means “You’re someone we’re always happy to see.” You can still call up and say “I’d love to stop by and see you on Sunday if that’s convenient.” If after several tries it just never seems to be convenient, you’ll know it was a hollow invitation.

I have spoken those words just a few times, and I really meant them. They meant: “If you show up at my door any time, day or night, sober or drunk, I’ll let you in, feed you, and give you a place to sleep.” I was speaking to my son’s closest friends during that nomadic stage when they were old enough to be on their own but not old enough to be settled yet, and they really were welcome to crash if they needed to. But I don’t think everyone intends the invitation that way.

Another vote for saying it and not meaning it, since I’ve only known one person who was then really ok with you coming over without notice or specific invite. And really, she shouldn’t have been ok with it in policy, because she clearly wasn’t ok with it emotionally. I sort of disregard it, same as when people I don’t really know that well ask me how I am, and would be put off if I said something negative.

Jeruba brings up an interesting point of using it as more of a crisis thing. Some people might mean it like this, though I think it’s important to distinguish it from the “I’m always up for hanging out with you” interpretation.

I say make a drama. “Oh my apartment is being cleaned right now, it’s so dusty and I don’t know where else to stay for temporary…” if they’re compassionate people they will invite you in. Or “Oh is that your cat, how lovely, You know I love bla, bla, bla…” until they invite you to come inside, usually for drink.

If you have close relationship with them just say that you would like to visit for short chat or whatever you want, they usually won’t mind at all.

When people say that i’m tempted to show up at their house at four in the morning with a calypso band & a shit load of balloons ;¬}