Yeah I think its fine, its a good run out for you to be 3 barreling with air in this spot, especially in a 3B pot, and you can definitely get called with worse. 

In fact because you’re OOP in the hand, unless you have enough history with the player to know that he’s going to shove his air or with worse pocket pairs on the river I think firing the last bullet is actually mandatory in this spot- hes always setting you in when he has aces and kings here, and you’re going to call it off,  but maybe he checks back hands like 88s TTs and JJs and 7x, that he might have called a shove with.

So I think that while checking might seem ok at first because maybe he’ll bluff with his air, I don’t think there’s enough air in his range by the river- and he’s probably checking back hands like AK/AQ close to 100%.  So not only does checking miss out on value but it gives him the chance to play perfectly against you which is a disaster. You played it perfectly in my opinion, GG.