AIBU to feel awful about this, and should I apologise?

Old fashioned saying “Don’t trouble trouble until trouble troubles you”. Stay quiet, lay low and read the room for a while. If it comes up, gauge the vibes and say something. You see if someone does tell her, these things have a habit of revealing themselves. If everything seems normal, let sleeping dogs lie! And don’t assume again 😆💖

Cashmere and Volvo sort vibe 😂
If you ever are in a wine drinking session with her it would be great for bonding!
[Shuffles closer] "Now, I had you down as the type to push a compulsory £20 teacher gift but then it turned out...." etc etc. Slightly slurry, conspiratorially, would be *chefs kiss.

I would learn the lesson and move on.If she ever finds out, I would say something like (I don't usually advocate lying but in this case it is damage limitation) that you didn't name her personally, and that you had been told it was her and as soon as you learned it wasn't you didn't say anything else. I think this will be less hurtful for her and less damaging for you. Hopefully it will all blow over.

But the lesson learned is the important part.

I have been negatively judged in groups of people without any warrant for it, more than once and for completely different, unrelated reasons. The way I dressed was one of them but for the others I honestly have no idea. I learned to grow a thick skin as it happened several times with different groups. It's not nice.

Only once have I had an apology of sorts from one judgmental b*itch (on a counselling course no less) who had made assumptions that because I was quite a gaudy, loud dresser who liked heels etc, that I was a bitchy, shallow oik who cared for nobody but herself. She found out via a different person telling her I was anything but, and I got an 'oh I didn't bother getting to know you, I didn't know you were like that! Shit!'

Not nice. And I am very mindful to be accepting of people regardless of looks and always have been, so I guess I learned my lesson in a different way!

There is no benefit to this woman in you telling her you've spread nasty gossip about her, if she doesn't know, is there? So the only benefit of your apology at this point would be to make yourself feel less guilty and as a preemptive measure in case it does get back to her, you've got your story in first.
So with that in mind, you'd do better by her in keeping quiet. Make sure those you maligned her to know you're wrong and hope that's the end of it.

Set the record straight with the parents you bitched about her to.

Tell them you got it spectacularly wrong and that you're very embarrassed at your actions.

No they don’t

This recently happened to me but in a workplace but I was the one being bitched about. Unfortunately the comments got back to me (a fall out between a couple of the other lady’s at work) and the lady has apologised to me. It was quite hurtful as the comments were nasty and totally unfounded. I’ll never really trust her again. I would speak to the women you have bitched to and say you were wrong and you really feel really bad. But I wouldn’t tell the mum as it will just be hurtful.

I'd say something to her directly with an apology before someone else tells her (theres always at least one that likes to stir the pot)

I'd make it my business to tell her you thought it was her and you are utterly wrong.

This is the cleanest way to handle it. You never know when someone you talked to will blab it out.

Ref the WA admin, have a word with her. It's stupid to spend so much on a teachers gift.

It's actually even worse that you did this to someone who is new at the school. You know when women talk about bitchy cliques at the school gate, that's actually people like you they are talking about. You could have just made her feel welcome and found out more about her, but instead you went straight to bitching about her and making stuff up about her to the other kids parents.

I definitely wouldn’t tell her I’d been talking about her behind her back. Just tell the people you spoke to that you got it wrong and it wasn’t her. You were happy to talk about her when you thought she was the culprit so surely you can’t have cared that much if it got back to her?

God. I thought (hoped) this kind of mental gymnastics stopped when everyone left their teenage years behind.

I guess it depends on the type of people we choose to surround ourselves with. Maybe you need better friends.

Speak to her, and thank her for arguing against it - you don’t have to give anymore background to your thanks. That way, if she ever hears about your bitching she’s aware that you found out that she wasn’t the instigator. And she’s had some appreciation for what wasn’t necessarily an easy position to take, even if she lost the argument.

On a more cynical note, she’ll assume anybody saying you were bitchy was, in fact, stirring.

They really do. They just don't admit it on MN.

They really don’t.

No, you've realised your error and won't do it again. If this mum seems off with you, you can apologise then. I f you do it now you are pretty much telling her she's the sort of person who would show off and cooerce other people!

You’d be telling her just to make yourself feel better. Absolutely no need.

Most people bitch about other people.

I like the idea of bringing up with the other people. If I knew someone who bitched like this I would wonder what they were saying about me behind my back and would distance myself from them.

I wouldn't say anything to the mum. I would say something in the Whatsapp group that £20 was ridiculous and I wanted no part of it.

If this is the perception I give from driving a Volvo, I should buy another.

Interesting that even though you know you were wrong you’ve sort of doubled down in your OP by describing her and implying of course you’d think that about her. If she doesn’t know you’ll look like a loon if you apologise. Maybe have a think about why you made the assumptions you did and why you are still attempting to diffuse that assumption by sort of implying she asked for it because she’s well groomed and drives a Volvo. Perhaps keep assumptions in your head going forward.