Glasgow host Edinburgh on Friday night in the RaboDirect PRO12 seeking to retain the trophy, which is decided by aggregate scores over the double header. The return fixture is on December 29.
Bradley said: "After the game at Firhill (in January) the Glasgow players weren't shy in letting us know they'd won it. We want to reverse that and that's what it's about."
He went on: "It's going to be very close. Both sides will be strong on the day and I've no idea how it's going to go, but I hope we win. They're derby matches, it's going to be a battle. We're looking forward to it."
The performance of captain Greig Laidlaw will be key for Edinburgh. The half-back will discover on Thursday if he will start at scrum-half or fly-half, depending on whether experienced Scotland centre Nick De Luca is fit to feature.
If De Luca is passed fit, Laidlaw will play at scrum-half; if not he will lead a reshuffled back line. Like French duo Morgan Parra and Frederic Michalak and New Zealand's Piri Weepu, Laidlaw is adept at both half-back positions.
Bradley said: "The common trait is the fact they're very good footballers, they're intelligent. I think Greig could play full-back equally as well. When you have a good footballer like him you want him involved in as much of the game as you possibly can. He'll be competent at nine and/or 10."
Laidlaw said: "I've played the majority of my rugby at 10 of late and I've had a couple of runs at nine. I'm very comfortable. I've trained in both positions through the week.
"We've picked up a couple of injuries within the squad, which is unfortunate, and Michael's not 100% sure where he wants to go with me, because of the injuries.
"We're seven points behind Glasgow. It's very important over the two legs to make sure we get something out of both of them. They tend to be scrappy affairs sometimes because everyone's getting stuck in so much. As a group of players we're ready for the challenge and we look forward to it."