Edinburgh travelled to Dublin on Friday with a starting XV unchanged following the 19-14 win over four-time European champions Toulouse in the last round on April 7.
The only switch in the 23-man squad was on the bench, where back-row Stuart McInally (hamstring) failed a fitness test, leading to a call-up for lock Steven Turnbull.
Four thousand fans are anticipated to travel as Edinburgh go in search of a place in the May 19 Heineken Cup final at Twickenham against either Clermont Auvergne or defending champions Leinster, who meet on Sunday.
"The size of the occasion and the backing from fans has not been lost on the players," Bradley said.
"Tomorrow will be a huge test. The hype, the intensity, the crowd, and the fact that we're away from home have a bearing on the size of tomorrow's challenge.
"Ulster are one of the in-form sides in Europe and will take great confidence from their two league wins over us already this season, on top of their away win over Munster in the quarter-final.
"Our form in this competition is such that we can rightly approach this match with a lot of confidence. The character and resolve of the players has been well tested in this competition and we have prevailed.
"It's a one-off game and the underdog tag is one we wear well as a team. Edinburgh Rugby have shown that we are a force to be reckoned with on big occasions and are relishing our first semi-final in this competition."
There was no place for Chris Paterson, Scotland's most capped player and record points scorer, who is set to travel with the squad and is poised to be on kicking tee duty once again.
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