My friend and I dropped our Slovenian rental car in Piran in mid-May. Online it seemed to show that there was a public bus to Purec where we planned to pick up our Croatian rental car. There was no bus available at that time. We went to the Information office near the bus stop (it's a stop not a station) where the very helpful young woman did some checking for us. In the end, we took a taxi for 60 euro from Piran to Purec. Piran was lovely, but it seemed (and please double check this) that Koper has consistent bus transportation to Purec.
According to Slovenian online sources (www.ap-ljubljana.si), you are correct. There is a Trieste - Pula bus line that has stops in Koper and in Porec, but not in Piran. The Ljubljana - Rovinj bus line, which has stops both in Piran and Porec, only operates between June 25 and August 31 (during the Slovene school holidays).