More of [noun] (not directly comparative)
How do you say "more of [noun]" without direct comparison. (Although it is indirectly compared to whatever the current status of the noun is, i.e. "more of the noun than there is right now.)
"I want to talk to more people." ("I want to talk to more people than I talk to currently.) I translated it as "Я хочу поговорить с более людьми." However, my Russian friend translated it as "Я хочу поговорить с большим колличеством людей." There's no shorter way to do it then how she translated it?

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Yes, as the previous commentor just said, the translation is getting quite long because of the case you need here. Yes, I don't see a shorter way, than "Мне нужно общаться с большим количеством людей." (I need to communicate to more people) or "Я хочу поговорить с большим количеством людей." (I want to talk to more people, note that there's only one "л" in "количество"). "Говорить", "общаться" requires a preposition "с", and you need an Instrumental here, and you have a preposition, so you can't just use "больше".
But if you want to say "I want to see more people" you can just say "Я хочу увидеть больше людей". This is Genitive. "I want to get to know more people" - Я хочу узнать больше людей.

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Perhaps:
More is Больше, более. Больший, Большая (last syllable is stressed), Большее is bigger.
Comparison is implied here, so you could omit it, if you want. 
Больше and более are employed with nouns in genitive case. Мне нужно больше людей для общения. 
If there are another case, e.g. ablative, you should use "Большее количество" (bigger amount). Мне нужно общаться с большим количеством людей.