The TV star - who presented the darts-based game show in the 1980s and 1990s - died on Wednesday morning with his wife Phyllis by his side following several weeks in hospital.
"He passed away very peacefully, [Phyllis] was with him. We are all shedding a tear", Pleus said.
The popular Sunday night gameshow mixed general knowledge questions with darts.
"By accident, Bullseye's catchphrases took off including, "Look at what you could have won", "keep out of the black, and in the red; nothing in this game for two in a bed" and 'BFH - your bus fare home'". It attracted 17.5 million viewers at its peak.
Born 20 August 1937, he was adopted by Joe and Annie Whittaker and moved from Cheshire to Lancashire.
At 15 years old, having left Accrington Grammar School, he worked as a dustman in Blackburn for a short time and completed national service before becoming a PE teacher. They had two children.
He rose to become a deputy headmaster but a stint in amateur dramatics gave him a thirst for being on stage.
Bowen began his career as a stand-up comedian in the 1960s but became a household name in the United Kingdom as presenter of "Bullseye", which ran for 14 years.
After Bullseye he had other TV work come his way, including as Hoss Cartwright in the second series of Peter Kay's Phoenix Nights, Jonathan Creek, Muck and Brass and The Grimleys, as well as radio and stand-up gigs.
He presented the show from 1981 to 1995, before turning his hand to radio where he ran a show on BBC Lancashire from 1999 to 2003.