One important thing to remember: If you discover that you've been bitten, there's a chance that you're carrying multiple bedbugs on your person, your gear, (and if you're traveling with someone close) your companion. Essentially, you've become a carrier. It's important that you think about taking care not only of yourself but other peregrinos. When you arrive at your next destination, you can tell the hospitalero at check-in that you think you've been exposed, and that you probably have bedbugs. I've never experienced a pilgrim being turned away because of this. In fact in the past, hospitaleros would generally go out of their way to help, by offering to clean your gear while you take a shower, supplying you with towels and some temporary clothing - and when my wife and I had our bedbug experience, the hospitaleros supplied us with some clean things which were "cast-offs" left by other peregrinos (we looked a little like John Travolta and Samuel Jackson in that memorable wash-up scene from Pulp Fiction) while we waited for our own clothes to wash and dry).
One reason hospitaleros are so eager to help is that bedbugs on a single person can actually lead to an entire albergue being infested and consequently closed until it can be completely cleaned. In the peak of the 2019 autumn season, at one of the major end points on the Frances, the local municipal albergue (with upwards of 90 beds - of a total of around 225 albergue beds in the town) was shut down with a bedbug infestation for a couple of weeks, which consequently made it near impossible to get a bed in that town for that entire time.
But the point is - you'll find on the one hand there's a lot of personal shame attached to getting bedbugs, and there's an inclination to keep it a secret; and on the other hand, a degree of indifference about what some people will consider only a nuisance. You have to make your own decision, of course, but if you do keep it secret, it's more than likely that you will spread the bug wherever you go. And if ignored, these little pests could increase and multiply at a biblical pace.
But that's the thing about the Camino. Almost every other person on the Way, particularly our hosts, will want to help you in any manner that they can, even if it's just to remind you that it's all going to be okay.