And doesn't matter if that person was walking, running, riding a bike or driving a car, right?Passing for me can involve someone/something stationary and someone/something moving past. Maybe I stood still to let someone (say a jogger) go past me (in the same or opposite direction).
Passing can also involve me going in one direction and someone else going the other way.
Only if you were in a race and you had bragged about how it would be impossible for a woman to pass you.When an AE speaker hears this sentence with no context at all, just a single sentence, would they know what is being meant?
"A woman overtook me and I felt embarrassed"
Without context it would mean nothing. You can't expect any rational reply to your question if you insist on an irrational question. If we were talking about driving, she overtook me, probably in a car or van, or on a motorbike. If we were talking about sitting on a park bench or going for a stroll, I'd think it likely that she was walking and went by me. If we were talking about a brisk walk in the park, or going for a run, she probably overtook me and was probably running. Not that I'd say "some woman".And if a BrE speaker hears the AE version, "Some woman passed me", they would think she was a passer-by and she passed me walking by, right?