Why inductive?
I see nothing wrong with having a plug of direct connection. Such things would need
to be locked down to prevent vandalism, but so will the inductive systems. The
shelters would need to be attached to the main grid and the solar power collected would be used to offset the power consumed.
As an alternative, you could have a power pack swap of some kind.
The side or bottom of the bus is opened, the pack removed, a fully charged one
inserted, and you are off. Packs would only swap when the one in the charger
has sufficiently more juice than the one on the bus. A well timed system could
easily swap out the packs in well under a minute if not a fraction thereof.