Learn Hardcore Japanese: muda ni matu zikan wo herasu tame, seki wo yoyakusita. - To reduce wasted time waiting, I reserved seats.

無駄 is a na-adjective. Adding に turns it into an adverb, so 無駄に means “wastefully/needlessly,” modifying the verb 待つ. So 無駄に待つ時間 = “time (that one) waits needlessly.”
Contrast: 無駄な時間 (adjective + noun) = “wasted/useless time.”

Is 待つ時間 natural, or should I say 待ち時間?

Both are grammatical, but 待ち時間 is the standard, set expression for “waiting time.”

待つ時間 literally means “time to wait / time (that you) wait,” and is fine.
A very natural rewrite is: 無駄な待ち時間を減らすため(に)、席を予約した。

Is 無駄に待つ時間 the best way to say this, or is 無駄な待ち時間 better?

Both are correct, but they frame things differently:

無駄に待つ時間 focuses on the action: “time you wait needlessly.”
無駄な待ち時間 labels the time itself as wasteful and is more idiomatic in everyday Japanese. Most natives would prefer 無駄な待ち時間 here.

Why is it 減らす and not 減る?

減らす is the transitive verb “to reduce (something),” which you use when you actively reduce an object (here, 時間).
減る is intransitive, “(something) decreases.”
So: 時間を減らす (you reduce the time) vs. 時間が減る (the time decreases).