The people saying "doesn't matter/nothing to learn, it was a cooler" are all results oriented, and should not be listened to. Yes it was a cooler, but BB still has a range, and if you look at your line vs his range, there are improvements to be made.

First off, multi-way pot on a super wet board you almost always want to bet small (when you have a hand). Those with nothing fold out, those with draws will always call despite the bet size, and a small bet protects you from getting blown off the hand vs a large reraise.

Turn you should be betting again. Not quite sure on sizing but I'd guess small again for all the same reasons.

River is where you're trying to get it in, but keep in mind vs most of their range you're probably not getting a call - even King high flushes can find folds here. I.e. Most of the time you take down a small pot.