Meyler scored the Tigers' second goal at the KC Stadium against his former club and celebrated by pretending to head-butt the corner flag in a tongue-in-cheek reference to his controversial clash with Newcastle United manager Alan Pardew last week.
Hull boss Bruce has commended Meyler for the way he has handled the fall-out from the Pardew incident and acknowledged the Republic of Ireland international is a firm favourite at the club.
Bruce said: "In the way he has conducted and handled himself this week David has been a model for me.
"David took it on the chin and accepted the apology. He didn't roll on the floor and he didn't go and bleat in the newspapers.
"He's had two horrible injuries and he's a former Sunderland player. He's chased something you would not expect him to get to but his determination and attitude has made him a firm favourite here."
Bruce's men confirmed their last four Wembley clash with Sheffield United when Matty Fryatt capitalised on a horrendous back-pass blunder by Lee Cattermole to net the Tigers' third goal in the 75th minute.
"Managers, coaches and players come and go but the people you have got to be happy for is the supporters," added Bruce. "It is quite remarkable that 1930 is the last time we were in a semi-final.
"I've said all along that it's sad that the FA Cup has lost a bit of the magic for whatever reason, but when you reach this stage it becomes exciting."
Bruce, who began his managerial career with an abridged spell at Bramall Lane in 1998, added: "Sheffield United gave me my chance in management a long, long time ago.
"I'm delighted for everyone. I've seen the scenes at Bramall Lane today and now we've got a big Yorkshire derby to look forward to at Wembley, which will be a magnificent occasion for everyone."