Nowt so queer as folk as they say in Yorkshire

Oreo If I suggested tea at her house I am certain she would say "Let's meet at the coffee shop". When I have called round prior to us going out in her car, the front door is locked and she is waiting on the deck.
Ziplock She once said she was embarrassed because her house, which looks lovely, is a bit out-dated inside ie the kitchen units. I think that's just an excuse though. The outside and garden look well-cared for.

Yes, I've a friend of some 35 or so years, who lives just across the road from me, and I have been in hers three times in all.

When we were young, people said she was worried that her place was a mess (which it wasn't) and the rest of the time, I have no idea why.

Sometimes, people are embarrassed to have people see their home. Do you think this could be a possibility?

You could try saying outright, ‘ let’s have a cuppa and chat at your house’ or ‘ y’know what Barbara? In all the years we’ve been friends I haven’t been into your house’ !
That has to provoke a conversation or excuses at any rate.
I think you’re entitled to know why.

I enjoy "A's "company but I see what you mean*Oreo*and admit I feel somewhat rejected.

Not sure you can really call her a good friend tbh if she hasn’t once invited you into her home!
I have a neighbour who is similar, wants to drop in for a coffee but doesn’t reciprocate, I make excuses now that I’m busy.Actually usually I really am, so not really a fib.