The archaic verb bate, meaning to lessen the intensity of, rarely appears in modern English outside the phrase bated breath. So unless you’re using bated breath, the word you’re looking for is probably bait, which has several meanings, including (1) something used as a lure, (2) to lure or entice, and (3) to taunt or ridicule. Baited breath is a misspelling.
Most often, bait means a lure used to hook or trap an animal, a sense often employed metaphorically—for example:
So when the news hit this morning that they were running a search for ”the world’s best bottom” we swear to God we tried not to take the bait. [Salon]
Bait may also mean to provoke, torment, or tease—for example:
Sharper played for Green Bay for much of Favre’s career there and will do all he can to bait him into making mistakes. [The Advocate]
Bate is sometimes mistakenly used for this sense of bait—for example:
For his part, Vilma said he’ll try to bate Manning as much as possible. [Boston Herald]