That should depend on:
- the child him/herself - if she's partially or fully emancipated
- the parents / legal guardians of the child (if any, as per above)
- all owners of all properties located along the route that child would take
- the school's policy
- any contractual obligations any of the above may be subject to
This would naturally create a network of contractual obligations that would both be more flexible and more effective than the current legal system. For example, their neighborhood association may have rules against kids riding bikes, schools may require that all their kids have health insurance, a health insurance contract may require helmets and knee pads when riding a bike, and so on.