In the short story "The Bet" why does the author take a long period of time for the bet to occur?

That's a good question.

In this classic story, Chekhov uses this extended time span for several reasons.

One of the simplest reasons is to raise the stakes, and to make the story more dramatic as a result. After all, the bet is on a man's ability to stay in solitary confinement. Isolation doesn't carry as much weight if it is for very short periods. (Imagine betting you could stay alone for a day, or an hour!)

 Making the bet for a number of years makes it much more important.

It also makes the changes the young man goes through more realistic. Given an extended time, you're going to cycle through a number of different moods and perspectives.

The length of the bet also carries other implications. This man isn't just trying to win money. He's giving up his youth to do so. When it starts, he is young. When it ends, he is mature/middle aged. He's a different person.