Bruce's side beat Sunderland 3-0 at the KC Stadium on Sunday to seal just Hull's second ever appearance in the cup's final four.
Goals from Curtis Davies, David Meyler and Matt Fryatt did the damage for Hull - whose fans marked the final whistle with a pitch invasion.
With Arsenal and Manchester City also lurking in the semi-final draw, Bruce could hardly hide his excitement at drawing League One outfit United - who booked their Wembley date with a 2-0 home win over second-tier Charlton Athletic earlier in the day.
"It's a great draw," he told ITV.
"Sheffield United are on a perfect run, they've beat everyone in front of them.
"But we've got to be honest, Sheffield United will say same as us, you want to avoid the big boys.
"That's the magic of the cup, it won't disappear. You get to the big quarter-finals, semi-finals and finals and fans and managers alike enjoy the occasion."
Davies capped a magnificent performance with a thumping header for the first goal and Bruce reiterated his opinion that the former Birmingham City man would be deserving of a place at the FIFA World Cup with England later this year.
Bruce added: "For me, he's been outstanding all year and he's a proper defender.
"He gets you an odd goal, there's always a shock and we're short at centre-back so why can't it be him, because he's a fabulous defender."
Davies himself was delighted with the result, but firmly stated his sights were set on securing another win at Wembley against their fellow Yorkshire club.
He said: "The club never been to this level in the FA Cup and I've never been there personally so it's a good day but we want to go the final.
"(I) can't say I was expecting that (pitch invasion), it was interesting!
"But we’ve got to a semi and we're delighted to go to Wembley but you want to go to finals and you want to win the cup."
