Translation:He wants to drink a little bit of water.
Ummm... and in the States too. You can count "bits" of anything, provided you mean a small amount. The word "bit" is not to be taken any more literally than "lot" in phrases like "a lot of water".
Some people are so prescriptive about language. Get with the pragmatics, y'all.
It has nothing to do with counting when you have a bit of something. In fact it is the opposite of counting. It means you take some of a larger mass of something. Like a bit of cake is just a part of a larger item i.e. there is no counting involved.
If you were dealing with something countable you would take a few of them, or even one of them but not a bit of them.
I am amazed that with such clear and understandable criticisms that this exercise has not yet been fixed. It can be a little water, some water, a bit of water, and a little bit of water in common English. I will say that some water is probably the more proper expression. You could also say a little water. The addition of a bit requires a countable noun but that nicety has been smooshed in spoken English.