Personally, I don't and I'm a native English speaker. I doubt many who weren't would have any chance of deciphering the meaning here either.

I see this usage fairly regularly. I'm not 100% certain of this, but I think it might be more common in Britain than America.

It's just an ellipsis. Or, as my first Google hit said:

"the omission from speech or writing of a word or words that are superfluous or able to be understood from contextual clues."

So: I would rather [have] a bus any day.

Is "I would rather you did..." odd too? Not a native speaker here :)

> Personally, I don't

That's more on you than the OP. It's hardly an unknown phrasing.

Actually, I didn't. It's an odd word choice, and 'prefer' would have made more sense. Rather is typically used in conjunction with another verb, while prefer isn't.