Bagman was once a Beater. Bagman was once accused of being a Death Eater about 13 years before The Goblet of Fire. When he retired from Quidditch he took a job at the Ministry of Magic as head of the Department of Magical Games and Sports.
Bagman loved betting, which got him in financial trouble. He paid some of his creditors (such as Fred and George Weasley) with Leprechaun Gold (that disappears). After the World Cup, some Goblins took all the gold he had and it still didn't cover all his debts.
To make it up, he made a bet on the Triwizard Tournament (which he was one of judges for). He bet the Goblins that Harry Potter would win. He tried to help Harry over the course of the Tournament and gave him a perfect score in the First Task even though he got hurt.
Though Harry touched the Goblet, Bagman didn't win the bet, the Goblins argued that Harry had tied with Cedric Diggory. Bagman now doesn't have so much as two galleons.