If these two had a couple of unfriendly run-ins, how long do you think it would take for Bruce to figue out that Parker has a type of pre-cognitive warning ability. That alone makes spidey different from any of bats' allies and enemies. What scenario would cause Bruce to suspect it.
Unless Spidey's screams his spidey sense is tangling, Bruce would be out cold way before he figures it out.
Now with PIS/CIS, Bruce figures it out in a second, another second he neutralizes it with his Spidey sense neutralizer, and in the third second Spiderman's out cold.