Kivrin only travels with the Doctor for a few weeks - relatively speaking, obviously. At first she thinks the Doctor's blank refusal to visit 1348 Oxford might be a race thing (but the Doctor proudly walks any time and place like she owns it), or that she might be worried about catching the plague herself (but she's not human); then the Doctor tries to explain about paradoxes, about fixed points in time, about timelines that can't be allowed to fracture.

And Kivrin decides fuck that; now that she knows how full of holes time is, she'll find some other way to at least save one of the girls.