Difference between “bunch of” and “group of” with regard to people

Solution 1:

I would say a bunch of people is informal. You can use it where informal writing is appropriate. Otherwise, choose another word, like group.

bunch (dictionary.com, definition #3)

Informal. a group of people: They're a fine bunch of students.

Update This update addresses the concerns expressed in the comments about when a situation calls for informal vs. formal styles in both writing and speaking:

When it comes to both writing and speaking styles, there is no strict dichotomy between informal and formal styles. There is really a continuous spectrum of formality and choosing your style depends on a number of factors. Here are some examples:

• If your speaking or writing audience is your book club, you probably can (and should) get by with a style on the informal end of the spectrum.
• If you want to convince an audience at the Royal Astronomical Society to take seriously your new and controversial theory on quantum gravity, you are going to need to stay at the formal end of the spectrum.
• If your giving a T.E.D. talk, people come to those to learn serious things in a fun way, so the formality will be mixed or in the middle of the spectrum.

In the end, you have to judge by your own experience with the audience you are addressing. My original answer above simply tells you that "bunch" is informal, and "good" is preferable when the needed style is not informal.

Solution 2:

Group tends to imply that the individuals have something in common -- they know each other, they work at the same place, they're all Americans.

Bunch tends to imply that the individuals are being grouped together more arbitrarily.

That breaks down in informal use, but if you're trying to find a difference that's the best I can offer.

Solution 3:

Is it appropriate to write in an essay A bunch of people or A bunch of friends?

If your audience/teacher/professor says no, that is the answer.

In theory, if someone says, "A bunch", the reader might want to know "how many?"

Likely, you were corrected as per "a bunch of carrots" vs "a group of people". Colloquially, you'd probably say a bunch of people came through the train station (indicating a great multiple of individuals over a period of time) vs a group of people met for coffee (indicating a simultaneous gathering of individuals). Especially, any formal gathering of people is considered a group. Meanwhile, a large aggregate (countable) number of individuals could be a "bunch" but more appropriately, one might be asked to clarify the number of the individuals if a "bunch" were specified.

Why would it be not acceptable to use bunch of people in an essay? Probably for the same reason that one should use the term murder of crows or herd of cattle. A group would be the more proper term for the gathering of humans.

For reference, check out a non-authoritative list of animal group names.

The comment from OP in my other answer:

Again, i would appreciate if you would explain the difference if it were spoken. Would it be appropriate for me to use I have a bunch of friends supporting me on this project.?

If it were spoken, it probably won't matter whether one uses bunch or group. For written, graded, or recorded purposes, for posterity reasons, one will want to attempt to use more formal language, especially when requested.