I'm a native speaker of English, and bunch of people does not sound wrong to me, nor do I suspect, to most native speakers (academics excluded; see below). The Corpus of Contemporary American English reports it used about a fifth as often as "group of people", which is certainly somewhat promising as far as it being "correct".
But I can't really say whether or not it is correct without knowing why the person who told you it's incorrect said that. It might be that it's considered rude to think of people as a bunch—I disagree, but if that's the case, whether it's right or wrong is going to depend on your specific audience.
Just in case, though, I checked the OED since it is far more knowledgeable than me, and interestingly enough, this seems to be of relevance:
3. A collection or cluster of things of the same kind, either growing together (as a bunch of grapes), or fastened closely together in any way (as a bunch of flowers, a bunch of keys); also a portion of a dress gathered together in irregular folds.
4. fig. A collection, ‘lot’. Also, a company or group of persons.
Definition 3 is the one that we're usually dealing with, and it seems to fairly clearly imply that bunch of people doesn't work, since people don't grow together (twins, triplets, etc. excepted) and usually aren't fastened together.
Definition 4 seems like it would work, but every usage it cites has bunch in isolation; it was never used in the form bunch of people.
I didn't see any other relevant definitions, so bunch of people may not be formally correct after all; either way, group of people is much more common and appears to be uncontroversial in usage.