As Scott says the Sainsburys bus operates at different times on certain days of the week.
On a Monday Wednesday and Friday there is a 1455 from the bus station to the store with a return from the store at 1210 & 1415
On a Tuesday and Thursday there is a 1220 and 1450 from the bus station with return times at 1400 and 1615. There are others but those are the ones that fitted in with a trip from up here.
2 of us went there on Thursday and caught the 1120 from Middlesbrough using 4713!!! arrival in Whitby was about 10 late which left plenty time to photo the P & R solos then caught the 1330 service 94 to Eskdale Estate which takes about 7 minutes, walked to the store in plenty time for the 1400 back to bus station. We decided to forego the pleasures of a return on 4713
and returned on the 4/X4 with 1432.
If you ring the Whitby store up and ask for customer services they will tell you what times the other services run.
The indicator showed S3 and on leaving the bus station it was heading for Lythe