My point is spider-Sense didn't prevent him from getting hurt there. Most notably it can be bypassed or tricked, and the methods for both are what Bruce is best at.
Spider-Sense is trickable in the sense that it is not CoO, it's just a tingling of danger on a general direction. However, it would require Batman both knowing about Spider-Man and preparing for it.
Otherwise there are other methods like big sound-based attacks or gas, but once again that requires preparation that the opening post forbids.
Just answering on how Batman can counter it in general, the setting for the matchup in this case favors Spider-Man.
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Let's say it's Peter from spiderman 1(the end) to make it more fair on bruce
Spider-Man 1 Spider-Man vs Comic Book Canon Batman?
Batman destroys that one.