Is there an inexpensive way to get from Rovinj to Pula airport early in the morning in the offseason?

I'm flying out of Pula airport (PUY) at 06:00 on Wednesday, November 18, and I'm trying to decide whether to spend the prior evening in Pula itself, or in nearby Rovinj (which would be preferable, as I'm in Rovinj for Monday evening). I'm not willing to pay the 50-60EUR a taxi from Rovinj or shuttle transfer would cost, so whether I spend the second night in Rovinj depends on the availability of an inexpensive morning link to Pula airport.

Is it possible to get from Rovinj to Pula airport early in the morning by public transit? I can find buses from Rovinj to Pula bus station, such as an Autotrans bus arriving in Pula at 05:15, but I wasn't able to find any which continued directly on to the airport.

If there's no public transit to Pula airport early in the morning in the offseason, is an 05:15 arrival at Pula bus station early enough to take a connecting taxi to the airport and make my flight? What if I don't need to check in at the airport (online check-in and no bags)? If not, are there any buses leaving earlier which would arrive early enough?