In order to go to Morioka from Miyako, there are two options now for the public transportation. One is riding a bus for 4 hours by taking the route of Miyako -> Kamaishi -> Morioka.
The other one is the train from Miyako -> Hikime (20 minutes ride,) and 30 - 40 minutes waiting time, then Hikime -> Morioka (2 hours ride.)
The total is 3 hours including the waiting time.
The earliest train leaves Miyako at 6:35 and gets to Hikime at 6:55.
Then there is a bus leaving to Morioka at 7:30, and it gets to Morioka at 9:24.
The latest one from Morioka to Miyako is taking a bus that leaves Morioka at 17:45, and it gets to Moichi at 19:35. Then, you can take a train that leaves Moichi at 21:14, and it gets to Miyako at 21:35. (Please see the 2nd chart from the link.)
Ref: http://www.iwate-kenpokubus.co.jp/archives/10302/
The other one is the train from Miyako -> Hikime (20 minutes ride,) and 30 - 40 minutes waiting time, then Hikime -> Morioka (2 hours ride.)
The total is 3 hours including the waiting time.
The earliest train leaves Miyako at 6:35 and gets to Hikime at 6:55.
Then there is a bus leaving to Morioka at 7:30, and it gets to Morioka at 9:24.
Ref: http://www.iwate-kenpokubus.co.jp/archives/10302/