Pretty sure one of the world's greatest escape artists would take the door.
Plus, the OP didnt say no regular gear.
Either way, thats how i see it going down.
Gender: Male Location: The Fortress of Solitude in Venus
Are the bears hungry?
Is there cubs in the cage?
In that case the female bears will go against everyone
Too many variables
If this is a real scenario which will be stupid that Batman and Daredevil will put themselves in that situation and in the real world no villain will be so stupid to create this trap for Batman and Daredevil to escape.
In any case in the real world I don't think Daredevil and Batman can FIGHT 20 Kodiak bears, however Batman might have some bear spray or some sleep gas.
So they can escape or win via plot device, but on a straight fight, they get killed, especially if the Bears are a coordinating their attacks which falls into the funny/silly realm.
Batman and Dare Devil win via pressure points. All the bears are paralyzed long enough for them both kick open the door open at the same time and stroll away in separate directions.
The bears get stomped. I don't even think they can damage Bats in the first place through his armor, and DD is way too fast (not that Batman isn't either). These aren't real people with limits, these are two impossibly skilled super humans who fight super super humans through sheer 'skill'.
Call me when a bear can kick through a thick ass healthy tree (being modest with Batman too) or could flip a limo.