need response ideas for my email to a "friend"

It does seem strange that it was her suggestion then she can't be bothered to turn up.

We all like to have a good birthday, I know how it feels if you have a disappointing one. My advice would have been to not contact her about her "no show". It's often better to "play the long game" and wait for her next move. She's not the good friend you thought she was.

We are all different with expectations about friendships. I'll quote a couple of examples from my own. There was a group of us who'd been at the same senior school. Yes, with hindsight, the friendship should have finished then. One escaped a dominant mother by going to uni. Cue outrageous behaviour, failure to contact anyone. She was invited to another's hen night though not the wedding. Again, behaviour unacceptable. Contact stopped with her at that point. The next issue when the married one had first child, remainder of group invited to christening. I went (was a godparent) but other friend used excuse of creosoting garden fence to not attend. End of that friendship.

Am I still friendly with the remaining member of the group, no. She became obnoxious and tried to rule my life as she did with her husband. Final straw was sarcastic comments about my niece. This friendship ended 16 years ago.

Just because she annoyed and hurt you, it's better not to react. As the saying goes "what goes around comes around". Know it's a natural reaction to respond angrily, but you're only sinking to her level.

I somehow thought she was only an acquaintance, a member in a group you had just met, that’s why I said to you not emotionally invest too much but take into account her behaviour.
I do agree with you that she disrespected you. And that speaks out loud of her.

Of course, I wouldn’t even send her a message to ask. She was the one who had to contact you.

I still don't get it. I mean, I am reading that she suggested the meeting, but I'm not reading that she set it up. If someone told me they're worried about corona, but really want to see their friends over their birthday, I'd suggest the very same thing. Doesn't mean I'd show up, cause that would just have been me politely attempting to soothe an aquaintances worries with a helpful suggestion.

Sorry if I'm being daft.

I subscribe your words. But, there’s a point. The lady should write to the OP to show interest in how the meeting went and say how she couldn’t attend for one or another reason. However she waits for the OP to contact her. It seems to me little caring from her part.

I’m not saying to put a cross on that person. Everyone messes up sometimes but, it’s something to consider if some other mean behaviour is repeated. The OP will be aware of a pattern from this person and the OP will know how to react from then.

Thank you for explaining
I think I'm a bit like that lady. I guess I'll keep this thread in mind the next time I face such a szenario. I know I could be more caring.

Apologies OP, I was being daft.