The Yorkshire rivals are battling it out at the top of League One and meet tomorrow at Valley Parade in a fixture which is traditionally feisty.
But Wilder – like opposite number Stuart McCall, a former player for the opposition – has told The Yorkshire Post he wants both sets of players to behave.
Premier League referee Jon Moss has been picked to take change, the Leeds official having shown 36 yellow cards in seven top-flight games this season, sending off two players.
Two seasons ago, Bradford’s Rory McArdle and Stephen Darby received red cards when these sides met.
“It’s a local derby in front of 20,000-plus,” said Wilder. “It will be a competitive game, we just want to make sure that it’s played in the right manner.
“Hopefully, it will be, if it’s refereed in the right manner, and both teams have a right go at it.
“Players have got a responsibility about playing the game in the right way.
“I don’t think supporters want to see players sent off, as we had at Scunthorpe (when Chris Basham was red-carded). This fixture has a history of players getting sent off.
“People want to see XI versus XI in front of a full house – which I think it will be, a big crowd – and both local teams going great.”
Wilder’s Blades have managed to combine some slick football with a steely determination this season, while Bradford were accused of “throwing themselves to the floor” by former chief Phil Parkinson when his Bolton Wanderers side met City this month.
When it comes to tough tacklers, neither Wilder nor McCall were “shrinking violets” in their playing days.
The Blades manager knows both sets of supporters demand 100 per cent from their players, and expects a typical Yorkshire derby.
“I want to see my team compete, and you have seen Stuart McCall play. He was a really good technical player and great passer of the ball but he weighed in, and made contact with the game,” said Wilder. “Our supporters want our team to do that, and having played at Bradford for a year, and knowing a tiny bit about them, they are a working-class club which gets right behind the team. They want to see their teams compete.
“Both teams are playing well, and we don’t want it altered by outside influences. You have to be disciplined. Even though it’s early in the season, there’s still a lot at stake. We will be backed by 2,700 supporters, and they will have about 18,000.
“It’s important we all keep our calm and the players get on with it.”
Bradford – who lost in the play-offs to Millwall last year – are second-placed in League One, with the Blades a point worse off in fourth but with a game in hand.
Wilder believes McCall has done a good job in taking over from Parkinson in the summer.
“Bradford have had a fantastic start to the season, are deservedly up there, and I believe they have been building over the last three years,” he said.
“Stuart has come in and added his touch. Sometimes that’s not the easiest when teams are going well. He has kept it going and moved it on.”
Wilder and McCall are both enjoying successful coaching careers but, in their playing days, featured for the opposition.
McCall spent five successful years at Bramall Lane, finishing his playing days there before embarking on life as a coach, while 49-year-old Wilder spent a year at Bradford in 1997-98 before ending his player days at Halifax Town.
Wilder has fond memories of his brief time at Valley Parade.
“I met the Queen when they opened the stand on the first day and won on the last day of the season to stay up,” recalled Wilder.
“It was a really good club, good crowds at the time, in the old Championship.
“I was there for a year, really enjoyed it, and met a lot of good people there.
“Chris Kamara was manager when I started, Paul Jewell was also there, whom I have a lot of respect for.
“Wayne Jacobs, who I knew from playing for Sheffield Boys as a kid, was a stalwart there.”
McCall, 52, played 71 times for United before hanging up his boots in 2002.
He said: “I had five fantastic years with Sheffield United and a lot of success during my time there.
“I had a great relationship with the supporters and the staff there.
“Chris has them playing very well at the moment. I remember watching their game at Gillingham earlier in the season when Billy Sharp scored a stoppage-time penalty and thinking that might be a turning point for them. It certainly seems that way.”
Marc McNulty – on loan at City from United – will not feature after the Blades rejected Bradford’s request for the striker to play.
McArdle interview: Page 22