Unless you're there watching him 24/7, its very likely you may never see him do it. Besides that big split, he otherwise doesn't look like a really bad chronic biter.....a fish like that will usually practically turn himself into a PK, so hes probably not a BAD biter. Just got a huge chunk of his tail one time, I had a fish that did that once.
A lot of things can cause biting, so if you really suspect that hes been nipping then its time to take a look at everything you're doing. Feeding schedule, tank size, amount of decorations, temperature, water change schedule, lighting and lighting schedule...everything. It could be the smallest most insignificant thing setting it off......or he could just be getting tired of his big, heavy fins. But you won't know until you look at every possible cause.
To me, what stands out the most is that just a stock of bamboo and a couple of moss balls is pretty sparse for a betta tank....they prefer a decent amount of cover to swim around/rest on. Did you notice the tattering of his tail in general getting worse/not better at all since you removed his other decorations?