There are several buses running from Muxía to Santiago, but I'd advise you to double- and triple-check the timetable on the bus company website (Monbus). When I needed to travel from Muxía to Santiago in January, the timetables at the bus stop and in the albergue said that the morning bus leaves at 6:30, but actually that day it was scheduled at 6:15 (the information was only available on the website), and I missed it.
But there is also a taxi service, and it's not terribly expensive, so you might want to consider this option. If you want to travel early in the morning, better arrange for a taxi to pick you up in advance, the day before.
Buen Camino!
