The human body has instinctive reactions to emotional circumstances, and one of these is how we breathe during times of apprehension or anticipation.
Our breathing often becomes short and controlled when we are in suspense or crisis.
Bated is a variation of the word abated, both meaning restricted or diminshed.
The word abated comes from the Middle English word “abatre”, which means to beat down.
Therefore, when someone is in a state of fear or suspense and his breathing becomes restricted, he is said to be waiting with “bated breath.”