Spiderman for a solid majority. Bruce gets a couple wins due to guile and being generally tougher/more capable than almost any "standard" human, plus gadgets.
Now (and not to feed into Bat-bois fandom delusions), if Bats has even a reasonable amount of prep (gadget-wise, from the Batcave and/or a day or two notice/suspicion for jurying something together), Spiderman might find some of his advantages (SS, for example) mitigated by some Bat-device, allowing Bruce a better set of wins.
In general, though, Spiderman for the clear majority.
Spidey for a clear majority!?
Yeah...sure, but only if Bruce has prep was well as a family sized portion of CIS/PIS backing him up...
A non-BS'ing...non jobbing...Spiderman litterally kills Bats with a single attack; all Spidey has to do is land a single punch and Bats is taking a one way trip to the graveyard.
Spidey for a clear majority!? Nay...Spiderman every single time under the conditions mentioned in the OP.