Hi
I biked the Primitivo last year. There is a gpx link in there if you are using a Garmin gps.
Having walked it, I found the cycling much tougher. When I walked, i went via Polo as Hospitales was clouded in, but with the bike, I did not want to go up down up down, and as the weather was clear, I pushed all the way to the top. From Tineo to Grandes was hard, it broke me, but the next day, I rode to Lugo, and from there, I had two easy days of 50ish Ks. It took me 5 days, but I was in a bit of a rush.
As for my bike, it is a 21 year old mountain bike that is very light with top of the line Shimano groupset. Tyres, were lightweight with a little knobbies, I did not want chunky tyres as I wanted to keep moving at a nice pace. I only have front suspension
Going it alone? I found that this way of travel was hard. I missed the cameraderie of the walk, where you all start and finish in the same place, and upon meeting someone, you know each other's life history in 3 hours !!! I did meet loads, but never saw them again, whereas my two walks, I still keep in contact with my fellow peregrinos.
Beds? No problems. I walked Primitivo in April, rode it in August and had no problems at either time. I never had to wait until 6, in fact, I have never seen a full albergue on that route.
Good luck with what you do, as for me, I fly to Sevilla on Tuesday to start the VDLP with two other cyclists