B is the only right answer. I see people write it as "baited breath" all the time, and IT'S WRONG. Do people think there's bait in the breath? To "bate" is to lessen, so it's sort of meaning you're holding your breath or hardly breathing in anticipation of something.

The others:

• A should be "couldn't care less," not "could care less." If you COULD care less, you care at least a little, don't you? Isn't that the opposite of what you're trying to say about how much you care?
• C should be "barefaced lie," though a long time ago it mutated from "barefaced" into "baldfaced," which was also misinterpreted as "boldfaced" or "bold-faced." This refers to people lying even without a mask on, which indicates how shameless those who do it are. (Lying about your identity or getting courage from anonymity to mislead was common in the days when there were masked parties.) So "baldfaced" is an understandable idea, but there's NO support for "boldfaced" or "bold-faced."
• D is a mangling of "all intents and purposes." Don't say "intensive." Please.