Learn Russian: Мы нашли ожерелье среди кустов.

It is in the Genitive plural because the preposition среди (among) always requires the Genitive case. The Nominative singular is куст (bush). Since it is a masculine noun ending in a hard consonant, its Genitive plural takes the -ов ending.

Could I use между instead of среди to mean "among" the bushes?

Not really. While English speakers sometimes mix up "among" and "between", Russian is strict here. среди is used when something is surrounded by a larger group, mass, or area (like a cluster of bushes). между means "between" and usually implies being positioned between two distinct things. Also, между would require a completely different case: the Instrumental (между кустами).

Is ожерелье in the Nominative case here?

It is actually in the Accusative case because it is the direct object of the verb (the thing being found). However, because ожерелье (necklace) is an inanimate neuter noun, its Accusative form looks exactly the same as its Nominative dictionary form.

Why use the perfective verb нашли instead of the imperfective находили?

We use the perfective нашли because finding the necklace is a single, successfully completed action with a concrete result in the past. If you used находили, it would mean "we used to find" or "we were finding," which implies a repeated or habitual action rather than a one-time discovery.