Breathing that is subdued because of some emotion or difficulty.
Which is it - bated or baited? We have baited hooks and baited traps, but bated - what's that? Bated doesn't even seem to be a real word, where else do you hear it? Having said that 'baited breath' makes little sense either. How can breath be baited? With worms?
There seems little guidance in contemporary texts. Search in Google and you'll find about the same number of hits for 'baited breath' as 'bated breath' - around 100,000 each. In one of the best selling books of all time - Harry Potter and the Prisoner of Azkaban, (whose publisher could surely afford the services of a proof-reader), we have:
"The whole common room listened with baited breath."
As so often, help is found in the writings of the bard. The earliest citation of the phrase is from Shakespeare's Merchant of Venice, 1596:
"With bated breath, and whispring humblenesse."
Bated is just a shortened form of abated (meaning - to bring down, lower or depress). So, 'abated breath' makes sense and that's where the phrase comes from.
Geoffrey Taylor, in his little poem Cruel, Clever Cat, 1933, used the confusion over the word to good comic effect:
Sally, having swallowed cheese Directs down holes the scented breeze Enticing thus with baited breath Nice mice to an untimely death.