Saying that Bulverism is a fallacy is simply to say that you can't refute someone's position by pointing out an ulterior motive they might have for believing in it.
Here's the way the whole thing works. Once an argument is given, the focus goes away from the person to the argument they use.
If someone gives an argument for the claim that smoking really doesn't cause cancer, then it isn't a refutation of their argument to point out that the person is paid by the cigarette companies. They might, for all that, have a good argument. Now if they are saying "I'm an expert, trust me, smoking really doesn't cause cancer," then the fact that they are paid by the cigarette companies is a problem. But if you can evaluate the argument, you should do that, as opposed to just considering the source.
If you don't like Lewis's term Bulverism, (since it comes from a Christian) just substitute ad hominem circumstantial.