...the only reason I can think of [...] to have him fight Bane in this instance is because he doesn't yet know just how formidable Bane is...
And that's exactly the point. A primary motif of the first half of the movie is that Bruce simply underestimates the threat that Bane actually poses (together with overestimating his own abilities that suffered tremendously from his age and the long break he took from "Batmaning"), both physically and metally. He thought he was nothing but a mercenary, a henchman to someone else higher up, that he could just interrogate to find out more. He underestimated both his strength and his dedication.
Alfred: You led a bloated police force on a chase with a load of fancy new toys from Fox. What about when you come up against him? What then?
Bruce: I'll fight harder. I always have.
Alfred: Look. His speed, his ferocity, his training. I see the power of belief. I see the League of Shadows resurgent.
Bruce: Bane is a mercenary. We need to find out what he's up to.
Bane: Peace has cost you your strength. Victory has defeated you.
Bane: Theatricality and deception, powerful agents to the uninitiated. But we are initiated, aren't we, Bruce?
Bane poses a physical threat to him that no criminal ever did before (as also reinforced by interviews from the film's Blu-ray) and which Bruce, against Alfred's warnings, just didn't expect, in the same way as Bane isn't susceptible to Batman's more psychological and tactical means of warfare. Neither did he expect Bane to actually have a personal vendetta against Bruce, he is "just a mercenary" afterall.
Christopher Nolan: In [...] trying to decide who the villain would be it was very important to me that it be a physical force. And a very directed militaristic force. And Bane seemed the ideal character to take on the physical threat to Batman.
Christian Bale: Obviously wanting to make sure that physically Bane is superior. And this is the first time that Batman has come across anybody who is superior.
So the answer to your question is that he simply didn't think it through enough. Yes, he was trapped with Bane in his own lair, but he was seeking him out anyway, so what did it matter? Seeking him out silently would have been better and the fact that Bane actually awaited him already should have put him off and reconsider the situation, but Bruce was blind to that. He still thought that Bane was trapped with him and not the other way around. He was both underestimating Bane and overestimating himself and was running into the fight blindly without knowing all the details or the level of Bane's dedication to his endeavour.
