I've passed bicycles whilst running, even on flat ground. But it was a family group. Those little kids were slow.

I'm sure I can run up hills as fast as I can bike up them, especially with all my heavy commuting junk. I don't even like to carry water when I run. And it sounds like the woman was doing hill intervals. The last time I did those, training for the Hood to Coast, I pulled a calf muscle on about the 7th rep. I don't usually run fast any more.