Do the monks believe the well in the valley of holliness stopped the first time be cause they bathed?
You can find this answer in Chapter 21. Now, it never says what the monks themselves believe, but you can certainly infer that they believe it.
The story says that as soon as they bathed, the spring stopped flowing. And then as soon as they abbot smashed the bath, the water started to flow once again. We are told that anyone who tried to take a bath there would surely get killed by the locals. He would be able to have his "halter" (noose) for free and would need it too.