Papagayo leaves Puerto Plata about 6:30. I have not taken it for a long time, but used to get it about 7, flagging it down when it was about to pass by Playero. I suggest you be beside the road by 7:10 pr 7:15 so you can flag them down. I prefer to be on the lookout early so never minded waiting if there a delay on the road between POP and Sosua.
He gets to Samana about 10:30, then heads back at 2. As was mentioned, he waits by the park. In the past it was in front of the Aduana and no doubt still is the starting point for the return. Depending on traffic on the highway and how long of a rest stop they make outside of Nargua, he is back to Cabarete 5:15-5:30 p m
Zurbs, this is not a bus line like Caribe Tours or Metro, it is one-man, one bus operation.
I believe there is also a bus that leaves Samana in the morning and returns to Samana in the afternoon. The people in Samana can tell you and where to get that bus if you don't want to wait until 2 pm to leave.