In my opinion, Bruce should be above average height or at least average. But since he surrounds himself with demi-gods, aliens, meta humans, etc, he's just dwarfed next to them. Like maybe about 6'1 or 6'2, but that's NOTHING compared to Diana '7'3 feet tall' Prince. Or Clark '6'9' Kent.
All the tabloids claim he has to be at least 5 feet tall because the only photos they can get of him are when he's next to his giant ass friends.
It is also my personal headcannon that all the robins stay shorter than him, except Jason, who should be at least 4 inches taller.
AU where Jason gets his revenge by becoming a lawyer and getting joker sentenced to the death penalty
Bruce is conflicted about it but any time he tries to say anything on the subject Alfred just talks over him like "oh we're so proud of you master Jason you finished college and you didn't even use your father's extensive resources that could've easily gotten someone in this family a degree aren't we so proud master Bruce that Jason got himself a respectable profession--"