Overall, I think DD will overcome The Man Who Broke the Bat. DD is close in capability to Batman in fighting skills, stamina, technique, and tenacity. While there are those who will undoubtedly point out that Bane took down Bats and thus indicates he is a tougher and stronger than the Dark Knight, there were extenuating circumstances behind that "defeat".
Everyone seems to forget that Bane did not engage Bats one-on-one in fair or equal combat. No, he used strategy to weaken him by running him ragged through a vicious gauntlet and then, when he was at his weakest was when Bane struck. Plus, Bane was an unknown when he fought Batman. He had surprise on his side and that counts for a lot. If you don't know what your opponent is capable of or how he fights, then you're at a major disadvantage. Bane on the other hand; researched, watched, and studied Batman in combat so he knew Batman's fighting style and prepared for it.
As a result, we have a villain who has a completely overblown rep as being the guy who broke Batman. Thus he MUST be a complete and total bad@$$ who is nearly the equal to Batman. I don't think that Bane has had that much success as a major super villain since his big debut. It sounds better that Bane has been able to decisively win against Batman since.
As this is a complete random encounter; Bane hasn't had a chance to research his opponent nor strategically weaken DD beforehand. DD is I think far superior in hand-to-hand combat, plus he's got his billy club. He can tell Bane is a BIG guy and he's used to dancing around, using nerve strikes and pressure points to whittle his enemy down. Bane resorts to his Venom enhancement but DD is used to fighting superhumanly strong opponents so is a bit more cautious and he can lock onto the Venom device is working to pump more of the Venom steroid into him and he'll probably go to disable it, despite Bane's attempts to protect it.
Bane realizes that he can't overcome his opponent so he decides to retreat, declaring that he'll be back to fight again another day. It's a strategic retreat and a victory for the Man Without Fear!