The Bagman family is comprised of Ludo, Otto and their father, the unnamed Bagman Sr.
Ludo was a celebrated Beater for the Wimbourne Wasps (c.1980) and later became head of the Department of Magical Games and Sports, until his somewhat informal departure from the Ministry in late June 1995. He was the announcer for the 1994 Quidditch World Cup final match (GF8) and also a judge for the Triwizard Tournament at Hogwarts during that school year (GF12, GF20, GF26, GF31). He also ran a rather unsuccessful betting service – and was still giving out odds during the Quidditch World Cup tournament in 2014 (Pm).
He got into trouble with the Muggle Artefacts Office because of an unusual lawnmower, but Arthur Weasley straightened things out for him. Out of gratitude, Otto’s brother Ludo then arranged the Weasleys’ tickets to the 1994 Quidditch World Cup (GF5, GF8).
"Bagman" = (Eng. slang) While in the U.S. this carries the sense of "one who collects money, as for racketeers", in the U.K. it carries the meaning "traveling salesman."