Or is boss correcting speech rude

Me and you both, @TeeedleDum

Or you know, you and me ...

It's not a rule.

You don't get to define universal rules based on your education and social set.

Professional linguists, when they look at this question, don't see a rule. They see a prescription, which they theorise is seen as a more prestigious way of speaking by its proponents, but which is abnormal (for "me") in actual usage.

In other words, this is more bouquet-not-bucket territory than a language error.

And that's the point of this thread. Native speakers sometimes make errors in formal standard English. This would not be an error even there.

Whether you can call any informal usage an error is less certain. But a huge amount of anxiety around language is caused by people parroting "rules" which are nothing of the sort. And it's not always in a helpful spirit - it's often an attempt to assert superiority.

I do this to my ex all the time so I’m rude too! Not the same example but just getting words wrong like ‘of coarse’ or ‘we WAS at the till’ or more frustrating, your for you’re & ALL the their/there wrong.

How on earth have you lived in the professional world and not picked up this rule!?
This thread is definitely a wind-up.

No, that's not a rule.

Some people learn that it's a matter of etiquette, but it's not a grammatical rule or a universal convention.

Native speakers tend not to follow artificial advice that messes with the rhythm, clarity and emphasis of their sentences. The "politeness" clause mentioned here often does that.

He saw me in my blue dress with my husband my husband. I hope you'll join me and my sister. Look at me and all my fine friends. I looked at myself and John standing side by side in the mirror ... All correct.

When people want to insist on good standard grammar, they should try to avoid adding their own preferences, conventions, or recommendations. Formal standard English exists, and can be learned and corrected. But it's not a grab-bag of everybody's pet peeves. And unfortunately there's a significant overlap between people who enjoy correcting others and people who elevate their habits and beliefs to rules that others should follow.

Grammar Girl used to have a good blog that respected that difference - here's a rule for standard written English, here's what lots of people think is a rule, here's a style choice. It's gone very ad heavy and jumpy. But you don't need much help, OP - and in terms of lunchtime conversation you don't need any. So I would trust her on the me-myself-I https://www.quickanddirtytips.com/articles/how-to-use-myself-and-other-reflexive-pronouns/. If going further I'd bear in mind that American English is more rigid about punctuation in some instances than British.

I know 'bob and I' is correct and I would use this whilst working (e.g in meetings or in emails) but when I'm on my lunch break I don't expect to be corrected

If you really would then I'd say there was no need for the manager to mention this at all

However you said that "grammar isn't my strong point", so if they've picked up mistakes in your actual work a few reminders might well be worthwhile

But it's normal and efficient for people to speak less formally.
It's not just the informality, though. Politeness and humility say that, when listing people, you always place yourself last. OP knows this but, nonetheless, puts herself first ("My boss will correct myself and other colleagues...") in conversation.
Like I say, it's not a good look.

Using language in the same way that others around you use it isn't wrong.

It's what language is.

Most conversations "in the wild" aren't in formal standard English. Generations of our ancestors lived and died and communicated without any standard language.

It's useful to know the rules of formal standard English for professional communication, since we are taught this version and it's a (loose) marker for education. But it's normal and efficient for people to speak less formally.

Some people are so pedantic they can’t help themselves. It is rude but…..

I’ve been in staff talent assessments where more junior people are being discussed for succession planning , additional training and supported development and judgements are made on appearance and speech.

And no I don’t work in the civil service

I don't understand why posters write Ddog or Dcat either, so maybe that's just me.

Do you really mean that you don't understand it? Or do you just mean that you don't like it? It is very common on MN for posters to claim not to 'get' things as a way of being sneery about them.

In case you really don't understand it... It is very common and normal for groups and communities (whether online or irl) to develop their own slang, terminology, abbreviations etc, often in a humorous or ironic way. It becomes a bit of an in-joke and using it makes people feel like part of the group.

It may be widely used but it’s completely wrong.

You are correct! ("Andy was meeting I" makes no sense. "I was meeting Andy" on the other hand does.) Sounds like your boss is correcting your grammar when there's no need! Also it's pretty weird policing the way you speak - he isn't your parent or a teacher. Seems like he's just trying to exert some authority over you.

"I don't understand why posters write Ddog or Dcat either, so maybe that's just me."

Dcat? That comes from Latin, surely? When I was at public school someone would always say grace before we ate lunch. They always said "Benedictum, Benny Dcat".

He’s comply wrong!

Its actually very simple; it’s “I” if youre doing the verb but “me” if the verb is being done to you.

I took a taxi
Bob and I took a taxi
The taxi took me to the airport
The taxi took Bob and me to the airport

Simples!

🤦🏼‍♀️

I'm glad I don't work with you.

Exactly. Everyone code-switches to a certain extent, depending on context and who they're talking to. Example right there in my last sentence. I'm a linguist. I know full well that technically it should be 'to whom they are talking'. Do I say that in casual conversation or on a chat forum? No.

If the OP is making grammatical mistakes when emailing clients or whatever, her boss is absolutely within his rights to correct her. If she's talking to a colleague in an informal context, he isn't.

I have a high standard of English and need to use correct vocabulary and grammar for my job. I reserve the right, when not in a direct work situation and speaking colloquially, to use the vocabulary, language and speech variations of the place where I grew up. Some of these might be seen as "poor grammar". I don't care. If this is your case then your boss is totally out of order.

Yes, this!

I was always taught to remove the other person from what’s being said, and if it doesn’t make sense, you’re using the wrong pronoun

Oik has connotations beyond grammar. It’s snobbery and dismissive. You may judge someone by their accent but don’t assume everyone else does.