Learn English – Why does “off limits” mean “not allowed to enter”

Compare:

Even people off to the sides of these stage speakers enjoy well-balanced, detailed sound...

to:

Even people to the sides of these stage speakers enjoy well-balanced, detailed sound...

In this case, there's the chance of misinterpretation if off is left out. It could sound like the people are directly at the sides of the stage speakers. Off to the sides, however, clarifies that there is distance at play and makes the sentence make more sense.

In other cases where it sounds unnecessary, it may be kept for sonorous purposes. In other words, we say it because it gives the feeling of the language flowing or maintains the rhythm of the sentence.

As another example, compare:

The attack came not from the monster before her, but from those off to the sides.

and

The attack came not from the monster before her, but from those to the sides.

In the first example, it's implying a long-range attack; are they shooting her with an arrow?

In the second example, it once again doesn't sound as far away. Maybe they're directly to either side of her or either side of the monster in front of her. In this case, it could conceivably be a close-range attack.

Bouncing an idea off a person means requesting that the person give a somewhat immediate response or gut reaction to the idea. Metaphorically speaking, the response bounces back to you right away.

It is rare to find the actual origin of a new word or a new sense of a word. I checked various standard references but found no known origin for this metaphor. The earliest use I found in print is the book U.S. International Business and Governments by Jack N. Behrman (McGraw-Hill, 1971):

The existence of these associations … permits government officials to know that, at almost any critical time, they can find an audience against which to bounce an idea or a new policy.¹

The quotation above shows that it is possible to bounce things other than ideas off someone. I think there is nothing wrong with “bouncing an opportunity” off someone. Alternately, you could “bounce an idea for an opportunity” off them, or “bounce a business proposal off them” if that is an appropriate restatement.