The phrase waiting time is both natural and common. The phrase wait time is sometimes used as well.
Ngrams shows that waiting time is the more prevalent of the two, but wait time has been gaining traction for the past couple decades.
As for the verbs and prepositions you've used, those are fine – English has quite a few verbs that can be (and are frequently) used in this context. If the original wait time was 17 minutes and the new waiting time is 7 minutes, you could say any of these:
The waiting time was...
- reduced by 10 minutes
- decreased by 10 minutes
- lessened by 10 minutes
- shortened to 7 minutes
When the numbers are 20 and 10, you can use either by or to, because the wait time is both reduced by 10 minutes, and to 10 minutes. Therefore, either preposition could be used in that special case, but those two expressions – while both true – would mean two different things.