The TV star, who was best-known for hosting the darts-based game show, was aged 80.
He presented a live morning magazine programme on Radio Lancashire from 1999 to 2003.
He taught at Caton Primary School near Lancaster before becoming an entertainer, attracting large television audiences with his North country humour, his cheery disposition and his infectious catchphrases in a show which ran virtually non-stop from 1981 to 1995. He died with his wife Phyllis by his side, according to family friend John Pleus.
"Bullseye" featured three pairs of contestants - with one team member answering questions and the other playing darts - going up against one another win big prizes such as speedboats, caravans, luxury holidays and cars, to smaller gifts such as darts or tankards.
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He became a household name when he began presenting Bullseye in 1981.
Mr Clayton, 65, said it would be "stretching" it to say he played a part in helping Mr Bowen get the role.
He also enjoyed cameo roles in dramas such as Last Of The Summer Wine as well as roles in Jonathan Creek and in Peter Kay's Phoenix Nights.
But he returned to the limelight in 2005, when he performed a solo show at the Edinburgh Festival Fringe about Bullseye, called You Can't Beat A Bit Of Bully.
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'I didn't show them I was proud of them, though I think they knew, ' he once said.
His agent Patsy Martin said to the Press Association, "I will very sadly miss Jim".
Bowen died two days after his hero. We are all shedding a tear. "He was a very lovely, genuine man". He also hosted a mid-morning show on 106.6 Indigo FM in Cumbria in 2009.
In 2011 Bowen suffered from two strokes, one at home and a second mild stroke in hospital.
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She expressed concern that the "repressive practices of previous military governments were returning at the norm once more". Adama Dieng said that if the evidence recently presented to him was proven, it would "constitute the crime of genocide".