'bunch' refers to a group: a bunch of bananas, a bunch of people. If you're referring to single sheets of paper, say handouts, try, 'a stack of papers'. If you're referring to a group of papers, say term papers, then 'a bunch' works.
As for subject verb agreement, note the article 'a'. It's singular, so the verb should be singular, too,
A bunch of papers is on the desk. => There is a bunch of papers . . . . Bunches of papers are on the desk. => There are a bunch of papers . . . .
The word "There" is an empty subject. It doesn't agree in number with the verb. In that kind of sentence, the true subject follows the verb. "a bunch" is the true subject.
You may take as many as you need it. (ungrammatical)
You may take as many as you need. (grammatical)