Ulster beat Edinburgh 38-16 last month, putting in a performance which head coach Bradley described as the Irish outfit's best performance in ten years, while in January they triumphed 42-20.
The Gunners have two RaboDirect PRO12 games on the road to contend with before tackling Ulster on April 28, the first against Leinster on Friday in Dublin - the host city of their European semi-final.
The second is in Cardiff against the Blues and head coach Bradley admits his focus is on fine-tuning Edinburgh's performance in preparation for the biggest occasion in the club's history a week later. "Ulster have beaten us twice this season and played very well," Bradley told the Scotsman.
"In fact, when the match in Belfast was over I went straight to their coach and told him I thought that was the best Ulster performance in the last ten years. They are a strong outfit with a lot of quality. They were pretty close to that level at Murrayfield as well, and they deserve to be where they are in a European semi-final. "Beating Munster in a Heineken Cup quarter-final at Thomond Park is a very positive credential.
That result didn't surprise me. "Like everyone else, I've been aware that Ulster are very much moving in the right direction, and they would have travelled to that match with a lot of confidence. >"But we're capable of beating everybody. If we play our best game we can win."
Guinness PRO12
Suite 208, Alexandra House,
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Ballsbridge, Dublin 4, Ireland