The Blues had rattled off an impressive run of five consecutive wins in all competitions before a weakened side, due to Wales call-ups, were beaten 52-9 by reigning champions Leinster.
Edinburgh have been on an impressive run of results recently, having won seven of their nine games in the Scottish capital, but a trip to Wales is traditionally a daunting one for the Scots outfit.
"Cardiff away will be a significant challenge indeed and is a match that will demand our utmost attention to every aspect of our game," said Bradley.
"We have a lot of respect for Cardiff, their players and the way they play the game. There is no hiding from the fact that they have favourable position to ours in the PRO12 and have already beaten us at Murrayfield this season.
"However, we must have faith in our ability, something which has been gathering steam in the past six weeks.
"Our season has a degree of momentum to it, with the recent wins in the Heineken Cup and good wins over the Italian sides, home and away.
"If we maintain the consistency of these improvements in this double-header then we are capable of achieving out goal, which is to keep our place at the top of this group and qualify for the knockout stages of the competition."