It is perfectly correct to say, “I was stood at the bus stop” — but only if someone picked you up physically, walked you to the bus stop, placed you down and stood you there.
It is just fine to say, “We were sat at the table in the restaurant” — but only if the waiter walked you over to the table, and indicated that you should sit there.
These are both completed actions, in the past tense.
If you are describing past continuous actions — which, let’s face it, is far more likely — then you need standing, and you need sitting.
Please use them. Please, please use them.
“I was stood there ages”, “I was sat there waiting” … expressions which sound ugly to my ear, which I know I use in conversation, and you might too.
Just don’t let them stray into your writing (notable exception: unless it comes out of the mouth of a character in fiction).
A published example hasn’t been easy to find, but here’s one in a story from the Daily Mail.
“Photographers also claim he was spotted outside the apartment that was raided with Kim inside and that he was stood there for two hours, constantly looking inside the gate and clutching his phone.”
Let’s give the final word to the Guardian Style Guide, shall we?
To invoke the present continuous this time: I’m not stood beside you on this one, GSG, but I am definitely standing.
Enjoy this mistake? Find many more in the eBooks 50 Mistakes Beginner Writers Make and 50 More Mistakes Beginner Writers Make, both available for £1.99 / $2.99 in UK / US respectively, as well as other Amazon sites worldwide.