Meyler chased down George Boyd's long ball to grab his side's second goal moments after captain Curtis Davies had given the hosts a 68th-minute lead.
And the former Black Cats midfielder celebrated by pretending to head-butt the corner flag in a tongue-in-cheek reference to his controversial clash with Newcastle boss Alan Pardew last week.
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 an horrendous back-pass blunder by Lee Cattermole to net the Tigers' third goal in the 75th minute.
Bruce added: "Managers, coaches and players come and go but the people you have got to be happy for is the supporters
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 the 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."
Sunderland boss Gus Poyet said he had no excuses after witnessing a dismal performance from his side just one week after their battling Capital One Cup defeat to Manchester City at Wembley.
Poyet made six changes to his starting line-up and watched the Black Cats struggle to create any chances of note before Hull's late burst saw them sink without trace.
Poyet said: "We didn't create enough but I'm not going to try to find any excuses.
"The players who played today were not good enough and that is simple - in the 50-50s, in the diving, in dealing with the referee when he panicked for 10 minutes - in not recovering well and not creating one chance."
But Poyet refused to pin any blame on Cattermole who was arguably at fault in the move which led to Meyler's second even before his back-pass howler.
Poyet added: "If you hide and you're not in the game and do nothing to take a risk, then for sure you're not going to make any (mistakes).
"That's the bad side of football - the ones that take responsibility and the ones that care, they are the ones who are in the position to make the mistakes - that's football."
Source : PA