Surely a poor question is a poor question whether the OP believes that or not?
Or do we just expect the normal voting process to have taken care of this before a bounty is even offered?
Yes, the expectation is indeed that the normal voting process should take care of most - if not all - problematic questions within the first 48 hours they were asked.
If a question survives that long, and thus becomes eligible for a bounty, the assumption is that there probably isn't a very good reason to close it. Or, that even if it's close worthy it isn't that bad that people can't wait for the bounty to be awarded (or expire) to vote to close it.
In the rare case that a featured question must be closed asap, a moderator can step in, refund the bounty and close it. If you think that's the case, then you should cast a custom moderator flag, and very cleary explain why the question must be closed asap.