Realistically I think people would find out Bruce is Batman so easily because (non-canon, obviously headcanons, fan-made, not from the comics in the comics Bruce is not like this at all but):
The man speaks in corporate talk, buzzword after buzzword
With the Justice League he casually talked about buying some dish he tried and another and another but every single dish costs more than a hundred bucks
When someone asks him a question regarding common household objects he answers with, oh my partner is in charge of that, which is how people think he has a house wife or a guy wifu you never know
It got to a point where Robin is answering those questions because otherwise Bruce would've been found out and Bruce had to train himself to not sound wealthy as Batman
And that includes not using super high tech but adorning it with wires and bad glue so it appears like he made it with stuff from walmart
Alfred had to take him to Walmart and force him to buy groceries with a hundred bill so he could understand why kids steal
Bruce is the type of person to have people do common stuff for him because he pays them so he had to get that trained out of himself
If he's near the police he cannot ask them for things, perhaps Gordon.
If he's with the batfamily, he has to command them but not physically buy them things because of their night work. That makes it sound like he's buying their labor and they do it for the love of the game
Now in this regard he gets more along with Tim and Damian because they use currency a lot to manage and control things. But with Dick and Jason its a no. He can have a transactional relationship with some but not the others. Although he tried it with Stephanie and she agreed which, surprised him.
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