I'd use the simple circumstance bonus.
This is not a pole-vault, it's more like using the stick to push off behind you as you jump to gain distance - sort of a horizontal pole vault.
She would get a bit extra heioght and distance, so the +2 circumstance modifier should work just fine.
This is assuming that the ground is rough to allow this to work and not have teh staff just slip around on the ground.
I'd do an actual untrained pole vault the same way - +2 modifier for the small amount of extra an untrained pole-vaulter could get.
A trained pole vault is an entirely different matter. I think you'd use jump with bonus from tumble. Given what you can do with a real pole vault, I think I'd allow it to be the jump + tumble modifers together. This would represent the rather large amount of height a pole vault can get you.
You would only allow this if you could tumble - that is, no encumbrance or armor reductions to speed.
Of course, all this is assuming a prepared site. Modifers would be, perhaps:
No surface/ smooth surface to grip the end of the pole: Impossible.
A rough surface: -10
Smooth surface with a wall/floor corner to plant the pole: -10
Rough Surface with a wall/floor corner to plant the pole: -5
Unprepared, but otherwise generally suitable site: -2