During summer season there is a weekly direct bus from Basel to Rovinj, the bus travels Fridays from Basel and arrive Saturday in Rovinj, you can see details in the table below. At other periods of the year it is possible to from Basel to Rovinj via Rijeka, where there are several weekly departure, you can see schedule for those bus here. In either case the bus travel time is about 16 hours. If you plan also to travel back to Basel, you might as well buy a discounted return ticket