ferries and scooters

I just booked a flight to Split (Croatia) for late June. We’re hoping to start in Split and island hop to Brac (Bol), Hvar (Hvar Town), Vis and Korcula (Korcula Town) and scooter around each of the islands to explore them.

I’m trying to figure out if I can book scooters for a week in Split or if I need to get them at each island separately.

It really just boils down to whether or not there are ferries that permit scooters that run between the islands.

It looks like it’s just the catamaran ferries that run between the islands – I know they don’t take cars, but does anyone know if they allow scooters?