"Barman", which is the more commonly used word in the Doctor Who universe and in the UK
Talk about it here.
A bartender or barmaid was an individual who served drinks, usually alcoholic, to patrons of a bar or pub.
Charlie was a bartender at the Last Chance Saloon in Tombstone, Arizona. He met Steven Taylor and Dodo Chaplet in October 1881. He was later killed by Johnny Ringo. (TV: The Gunfighters)
Brad was a bartender at the Golden Gopher in 2011. After meeting Jack Harkness at work during the time of the Miracle, they went back to Brad's apartment and had sex. (TV: Dead of Night)
Henry was the manager and occasional bartender at Bianca's Cabaret, an exclusive nightclub that offered drinks and entertainment to clients from all over the universe. (AUDIO: The Wormery)
Guinan was a time sensitive native to a parallel universe. She worked as a bartender in the 24th century in the USS Enterprise-D's lounge and recreation facility known as Ten Forward. (COMIC: Assimilation²)