Holding one’s breath back in expectation. To bate meant to restrain, but this verb is scarcely heard today except in this cliché, which itself has an archaic sound and often is used ironically. Shakespeare used it in The Merchant of Venice (1.3): “Shall I bend low, and in a bondsman’s key, With bated breath, and whispering humbleness.” A more recent colloquial locution is don’t hold your breath, meaning “don’t wait in vain.”