I think it's pretty clear. The end of the plot summary on the linked (Wikipedia) page notes that the ring that remains behind when she disappears is "chipped and charred."
That means that the ring, and hence that instance of Bunny herself, must have gone through the plane crash. So in her personal timeline she gets on a plane to Rome that crashes; that's already happened and she can't change that. Somehow the event of the crash causes an image/alternate of her to reappear in the past and the (suppressed? subconscious? not shown to the viewer?) memory of the crash causes her to visit her hometown instead of going to Rome.
(Note that I can't tell if she doesn't remember the crash, or the audience is just not told that she does. The device of the images she sees in the ring might simply be a way to justify her urgency to the audience, while keeping the stinger secret.)
Once in her hometown, it is important for her to prevent as many people on the ground from dying in the crash as possible. None of the outcome of the crash (on the ground) is known to her, so this portion of her timeline is still malleable, and she tries everything she can to keep people from going to the picnic where the crash will occur.
Once the crash happens, the loop in her timeline closes and she vanishes, leaving only her dead body in the plane.
Ultimately she can't change her own fate, but she is still given a chance to save others.
I found a very complete analysis of the episode that focuses mostly on the storytelling, but does dig a bit into the timeline aspect.
