Can anything be "bated" but one's breath?
Solution 1:
Yes. Aside from its meaning within the idiom "with bated breath," bate as a verb can mean 1) to moderate or restrain, or 2) to lessen or diminish, among other definitions.
To give an example, as you can see in this dictionary entry, one can have bated sentiments such as bated enthusiasm or bated hopes:
An example sentence here would be "After waiting two and a half hours in line for the Empire State Building observatory, we finally trudged into the elevator with bated enthusiasm."
It would seem that many things can be "bated," so long as it makes sense for it to be moderated, restrained, lessened, or diminished. There is even a proverb that goes "In the report of riches and goodness always bate one half."