Suit jacket - when travelling on a bus or train

[SusanOldknow]

I have a query which maybe someone has a good answer for !

About twice a month, I have to go to a formal all-day event for work - the dress code is standard office suits, and I will wear a trouser suit. I get there by either train or bus. I find once I am on the train / bus, it's typically too warm for me to want to wear my suit jacket, plus I don't want to get it crumpled during the journey. (I tend to run hot in temperature plus menopausal hot flashes mean I'm usually hot rather than cold).

Is there a clever way to fold / carry / manage a suit jacket so that it doesn't get crumpled? Does anyone know of a bag that would be suitable to put it in, when gently folded, which would protect its shape but be small enough to work on a train or bus ? (Suit carriers are too big for bus travel).

Intercity trains usually have a little hook above the window that is there for suit jackets!

If you're getting a local commuter service there may not be one. Can you not just fold it neatly and put it in a large carrier bag that you sit on your lap? You could put a piece of cardboard in so it stays flat.

Thanks @Mulledjuice - I should have said, not intercity so no hook. I like the idea of the piece of cardboard - could be a good low-tech solution