Already you said she rides around the neighbourhood, etc. --small mileage. Already she can balance on a bike and go. There are many adults who cannot balance on a bike at all.
She does not appear athletic to you, however it is interesting she has approached you (or at least someone who demonstrates experienced cycling a 'higher level').
While you help her hunt down a hybrid bike to borrow, to find out from her why she would like to cycle 'better'. Is it strictly for techniques to help her enjoy enjoy cycling, etc.? (she already knows how to cycle in a basic way) Ask her if she wants to go abit farther to do certain errands, explore places.
In terms of learning gear shifting...have her shift and ride comfortably first on flats in parking lot or in a park with paths, within 1-3 different gear changes. And help her understand that she should change gears as often as she needs even if she is going for only 5-20 miles...to make herself more comfortable and efficient as a cyclist. If she experiences back pain, all more the reason she doesn't overly push on her gears. Then later, you might need to ride with her to deal with gear shifting on small hills, etc.
Show her several designated bike routes and any local bike maps. You would amazed how much people appreciate this.
Showing her a few basics on better /safer cycling on road with bike, would be helpful also.
She sounds like she just wants some better fun, more independence and maybe more exploring which might translate into further distances.
Note: Suggest that she see her doctor /physiotherapist to recommend exercises/anything else for her back pain. Like many people in cycling, if you don't do safe stretching exercises for back, all over body flexiblity, etc., one will be plagued with back pain.




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