The reason your'e having a problem is because of the great distance between the two and because
Sarria isn't a big place and to reach it from most places you need to get to Lugo first and then travel to Sarria.
There is only one train a day from Logroño to Sarria - it leaves at 1:05 in the morning and arrives at 7:40am
http://www.renfe.es
You can get an ALSA bus from Logroño to Lugo (there are only two a day) and then take another half hour bus to Sarria from there.
http://www.alsa.es
Logroño to Lugo 2:15 10:00 7h 45min € 34.74
Logroño to Lugo 16:15 2:10 9h 55min € 34.74
If you have a day to spare, you could get a bus to Leon :
Logroño Leon 15:15 19:25 4h 10min € 20.67
And then get a morning bus to Lugo - there are buses almost every hour from 07h30
Leon Lugo 7:30 13:00 5h 30min 22.8 €
Leon Lugo 8:30 13:00 4h 30min 22.8 €
Leon Lugo 9:30 13:00 3h 30min 22.8 €
Leon Lugo 10:15 13:30 3h 15min € 16.08
Leon Lugo 10:30 15:50 5h 20min € 17.19 € 32.68
From Lugo you would take one of the frequent buses to Sarria on the Monbus
http://www.monbus.es/
These buses all leave from the same bus station in Lugo so it isn't difficult to find the correct bus.
Lugo is a lovely little town with the best preserved Roman walls in Spain. It would be worth spending a little time in the old quarter (right next to the station) before moving on to Sarria.
Good luck!