The Scottish side have an unchanged starting XV from their stunning 19-14 quarter-final win over four-time European champions Toulouse on April 7, while the only alteration to the 23-man squad is on the bench where back-row Stuart McInally (hamstring) has been replaced by lock Steven Turnbull.
Ulster, European champions in 1999, quarter-finalists last season and twice comfortable winners over Edinburgh in PRO12 competition this term, are highly fancied to advance to the May 19 final at Twickenham.
But Bradley's men have defied the odds time and again in Europe this term and are optimistic of doing so again.
"It's easier going in as an underdog. It is an advantage to us," Bradley said.
"You know you have to be as sharp as you can be to match the opposition."
And Bradley sees no reason why Edinburgh cannot beat Ulster and then go on to defeat Clermont Auvergne or Leinster, who meet in the second semi-final on Sunday, to lift the trophy.
"You're in a final and the same thing goes - if we have a good day there I think we can win the cup," he said.
The former Ireland scrum-half, who was installed in the Edinburgh hot seat last May, added: "The resilience of the lads has been excellent.
"Against Toulouse there was only two points in the match up to the last kick of the game and we were trailing at half-time, but we managed to hold Toulouse scoreless for 50 minutes.
"These are the pillars you build confidence on."