I did the Camino 2010 and 2011, and in both cases I was attacked by bedbugs without any consequences.
Before going to the camino I sprayed all my clothing, backback, shoes, matress, sleeping bag with permethrin (in Portugal and Spain you can try to find a product called Biokill: it's a pulverizer with 99%water 1%permethrin) Permethrin only attacks cold blooded insects, so humans, cats, dogs, are totally safe. Do not dispose water with permethrin in sinks, or water-streams because it's deadly to fish. Permethrin also keeps active in your cloths after several washes.
Then I bought a plastic sheet (try to buy a thin plastic that doesn't make noise) and took with me some paper disposable sheets to put in top of it. I did my camino in the summer so almost didn't slept in a closed sleeping bag. Both of these items were also treated with permethrin. This is a very lightweight solution.
You should always check your bed surroundings, as stated on other posts. If you think you found bedbug signs go talk with the albergue owner immediately but at least until you got a confirmation try not to alarm everyone. If you don't feel safe, you can always try to sleep somewhere else.
I was attacked several times but never got bitten. Each day I inspected my sleeping bag and some times (3-4 ocasions) I saw dead bedbugs that managed to descent from a top mattress, or crawl from walls, wooden bed frames..etc. As soon as they touched the some of my stuff they died. Then I reported to the albergue owners. What they do is to seal the room for a cleaning crew to disinfect everything. Most albergues have contracts with specialised companies for this.
This is very important: when you arrive in order to prevent future bedbug problems do not put your cloths/gear in contact with other house clothing, carpets, sofas, etc. Put everything in a big plastic bag, take care of yourself, relax, and then do the washing
I pulverized my sleeping bag once again just to be sure and then stored it.
I try to think of them like mosquitos, everybody is more or less used to mosquitos, I find mosquitos much more menacing than bedbugs because the little bastards can fly
So, mentally at least for me, bedbugs are not something that prevents me from a good night of sleep.