Bowen presented a morning radio show for Radio Lancashire between 1999 and 2002 but resigned after making a racist remark on air.
The former deputy headmaster, who was born in Lancashire, began his career as a stand-up comedian on the club circuit in the 1960s.
Bowen fronted the much-loved show from its inception in September 1981, right through to its final episode 14 series later in 1995.
At its peak Bullseye enjoyed up to 20million viewers, with three sets of contestants made up of a "knower", who would answer general knowledge questions, and a "thrower", who would throw the darts, competing for prizes.
The advent of Granada TV's The Comedians gave him the opportunity to appear on national TV, which helped persuade him to become a full-time entertainer.More news: Nate Solder leaves Patriots to join Giants on 4-year deal
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He also scored a number of acting roles, appearing in "Jonathan Creek", "Phoenix Nights", "Muck And Brass", "Last Of The Summer Wine" and "The Wheeltappers And Shunters Social Club", as well as appearing on the ITV sketch show "You Must be Joking".
His agent Patsy Martin told the Press Association: "He has sadly died".
"I watched seven hours of Ken Dodd and I watched him completely decimate 7,000 people". He left them in ruins with laughter.
'I've got £100 here and it'll take me two minutes to count out'. "We are all shedding a tear", said his friend Pleus. "And so I learned his act".
In 2011 Bowen suffered from two strokes, one at home and a second mild stroke in hospital. He also hosted a mid-morning show on 106.6 Indigo FM in Cumbria in 2009. "He was a very lovely, genuine man".