Several years on from their initial meeting, though, the venue has seen the opening of The Nap, a comedy thriller that stars '71 and Unbroken actor Jack O'Connell as Dylan Spokes, a local lad on the verge of winning the World Championships and losing everything he's worked for.
What changed in-between to alter Bean's perspective was the same thing that changed the way many saw the game - match-fixing.
In 2013, the former world number five Stephen Lee was found guilty of seven charges in what officials called "the worst case of snooker corruption we've seen".
That, and other cases involving the likes of John Higgins and Joe Jogia, gave Bean the impetus to create the story and the characters he had been looking for.
"I couldn't think how we could have a play about snooker for a couple of years, but then there were a few match-fixing scandals and I came up with the idea that if the plot was driven by a scandal, that would give us the opportunity to have a professional snooker player in the cast.
"So Dylan would have to play a match against a snooker player who has got no lines and if the audience knows that Jack is meant to be 'tanking' the frame, then that would fit the plot and we'd still have a game of snooker in the play.
"Richard was happy with that and so I went away and wrote it."
He says Wilson's idea was to "marry two audiences" that use the Crucible - snooker fans and theatregoers - and "get a few more blokes into the theatre".
Even after he had agreed to write it though, Bean said he still was not convinced.
"I said it was a brilliant marketing idea, but a rubbish idea for a play because actors can't play snooker.
"It's one of the most technical sports there is.
"We all play it badly and we all think it looks quite easy and then you find yourself with a cue in your hand on a full-size table and it's utterly daunting."
He says the writing process involved him joining a snooker club and playing on a regular basis, to get an insight into how hard the game is.
"In the afternoons, I would go down to the club and hire a table and play a few frames against myself, to study the art of angles.
"In the play, there's an invention called a sighting ball - a white ball covered in colour polka dots.
"I came up with that while playing. It helps you learn where to hit the target ball to pot it.
"It allowed me to get into the game in a technical way."
The play did not just require him to get to grips with the sport though, but also with the city that has been the home of the World Championships for four decades - Sheffield.
"I was fortunate that an actor I have worked with several times - Robert Hudson - is Sheffield born and bred.
"He was born down the Eccy Road (Ecclesall Road, one of the main arteries into the city) and still lives that way.
"He talked me through the intricacies and esoteric stuff about Sheffield and guided me on where Dylan would have been practising and living."
That local knowledge runs richly through the finished play, with references to Snig Hill police station, the Hathersage countryside, Manor Top snooker hall and Netherthorpe coming thick and fast.
Source: World Snooker
For all the local references though, the easy humour and pace of the play mean it feels like the writer's best known work, One Man, Two Guvnors.
Bean cannot see the similarities and says thoughts about the popularity of that play were something he tried to get away from when writing The Nap.
"The success of One Man, Two Guvnors confused me, to be honest.
"I don't regret it at all but you think 'the next play, should it be like One Man?'
"I tried to do a couple of things that were like it and they didn't work - my advice would be: if you have a big success, the next thing you do should be completely different.
"This is totally different. Richard [Wilson] said he can't think of another play that has got the thriller element, the comedy and the live sport that this has got."
The play really does have live sport - O'Connell's opponent on stage is John Astley, who has been ranked as highly as 75th in the world, and on more than one occasion, the actor is called on to make difficult shots on the exact spot where some of the game's greats have played.
That means things do not always go to plan, because as talented as O'Connell is, sometimes his shots go awry - something Bean says he had to consider while he was writing.
"I didn't quite know how to structure the end, other than giving Jack the stress of having to pot the pink and the black.
"Of course, the easy option is to write a different ending but I then realised it doesn't matter if he loses. When he misses, it changes the play, but it is still a legitimate ending.
"So we've got two endings and we never know which one it is going to be."
Thankfully, he says O'Connell has been successful on stage - much to the pleasure of the audience.
"He has already sunk an incredible black, worthy of the best snooker players.
"I was watching and didn't expect him to get it, but he potted the damn thing.
"The place went crazy, as if a young Sheffield kid really had won the World Championships."
With the city still waiting for its first real homegrown world champion, a victory for Dylan Spokes and for a play that celebrates one of its favourite pastimes will just have to do for now.
The Nap runs at Sheffield Crucible until 2 April.
When Sheffield Crucible associate director Richard Wilson approached playwright Richard Bean with the idea of putting on a play there about snooker, the sport that has made the venue internationally famous, he was against the idea, as "actors can't play snooker".