I got on a minibus and awaited departure.

awaited (more literary/formal)
waited for

A man sitting beforein front of me stood up andto change to another seat behind me.

Behind me was sitingsat a girl.

Or: A girl was sitting behind me.
I don't know why, but the word order in your phrase is weird with the past progressive

“I suppose the trip will be more pleaserant for you, if I’m near to you”,” the man said and takeook the seat next to the girl.

In English, all punctuation is within the quotation marks or parentheses, and there is no need for a period if there is a ! ? or . inside the quotation marks or parentheses. For example: She asked: "Should I come with you?"

I hadn’t seen at her when she gothad gotten on the bus, but judging onby her voice she iswas [maintain past tense throughout] young.

Or: I hadn't seen her get on the bus. This version means you didn't see the action of getting on the bus; the other one emphasizes that you hadn't seen her. Both work here; the difference is subtle.

I suppose she was a postgraduate student or a young teacher and that he was some kind of a professor at the same college or university.

a is optional in "some kind of a professor" With a=more formal
college=university more or less, so pick one to avoid redundancy.

The man was glib.

Glib is a rather rare word. If you choose to use it here, you should change all the get/got/gotten to stronger, more interesting verbs to match the style.

“… each woman is genetically programmed to change her partner from time byto time, so I prefer to be infantile, because a woman would/will never leave a child…”, the man talkesaid and the girl laughed again.

talk cannot include what is being said; said requires that you include what is being said.
He talked loudly about __________ but not He talked loudly "___". He said, "____" but not He said loudly. as its own sentence without the quotation.

It’ is a funny idea, by the way.

If you're going for a more formal tone (as your other sentences suggest), you should write out all contractions.

It’ is hardly true.

Perhaps add a transition here? Additionally/Above all/Of course, etc.

I got on a minibus and waited for departure.

A man sitting before me stood up and changed to another seat behind me.

I think "sitting in front of me" sounds slightly more natural.

Behind me wasThere was a girl sitting a girlbehind me.

this sounds more natural

“I suppose the trip will be more pleaserant for you, if I’m near to you”, the man said and takeook the seat next to the girl.

or "the man joked"

I hadn’t seen at her when she got on the bus, but judging onby her voice she iwas young.

or "looked at her"

I suppose she was a postgraduate student or young teacher and he was some kind of a professor at the same college or university.

some kind of mistake / some kind of doctor / some kind of textbook - I think there's never an "a" in this structure

“… each woman is genetically programmed to change her partner from time byto time, so I prefer to be infantile, because a woman never leaves a child…”, the man talkesaid and the girl laughed again.

If it's linked to a specific statement, "talked" sounds strange. If you don't want to repeat "said", you could say: claimed/shared. Or more formally: announced/declared/stated.

A Gentle DallianceAffair

I got on a minibus and waited for departure.

A man sitting before mein my front stood up and change another seat behind med his seat.

Behind me, a girl was sitting a girl.

“I suppose the trip will be more pleaser for you, if I’m nearant if I’m sitting next to you”, the man said and takeook the seat next to the girl.

You're saying the story in the past tense, the verb should be in the past (took)

I hadidn’'t seen at her when she got on the bus, but judging onby her voice she iwas young.

I suppose she wais a postgraduate student or a young teacher and he was some kind ofis a professor at the same college or university.

You think that's their current occupation, it should be in the present tense.

The man was glibsmooth.

“… each woman is genetically programmed to change her partner time by time, so I prefer to be infantile,mmature because a woman never leaves a child…”, the man talked and the girl laughed again.

You sure the girl laughed 🤨?

It’s hardlynot true.