I think what you mean to ask is, is this about having skill/ability, or having permission?
The answer is that this is an isolated sentence in a language learning program. Absent any other clues, we should translate "kan" as "can".
Strictly speaking, that means you are asking about skill or ability, not permission, which in English would be (strictly speaking) "May she ride a bike?"
"kan" means "can", "being able to", this means both having the skill AND being able to.
If someone doesn't know how to ride the bike, they 'can't' bike anyway, if they know how to then asking "kan" is asking for other possible obstructions. You might not be able to cycle because there's not enough time and you have to go by car, because your bike is broken or because you have an injury.
When asked in general "kan zij fietsen" it might be understood as 'does she know how to cycle'. If you know that someone knows how to but you want to know about the circumstances, you can add some indication of time: "kan zij vanavond fietsen? (Als het donker is)" or "kan ze nu weer fietsen? (Nu haar been uit het gips is)".
For having permission we use "mogen" - "zij mag fietsen" (the doctor cleared her, her parents are okay with cycling in the dark, whatever).