Albergues with private rooms?

Check on gronze.com. More and more albergues have added private rooms.

at the top left corner of this page, the first tab/category is Camino Guides, click it. I have experience with the Brierley guides (those with photograph or map background on front cover) and the Wise Pilgrim guides (solid color background and block letters). There are more guides and different authors offered on that page as you scroll down.

At the beginning of the Brierly and Wise Pilgrim guide, you can find a Legend page in the front of the guide that tells you if the Albergue has private rooms. The Brierley guides have a small red colored + sign and the Wise Pilgrim have a single bed icon per picture below.