I know that the appeal of the Brucie Wayne identity is shameless incompetence covering up extreme hypercompetence, but another interesting aspect of Bruce's in-between persona (not quite public, but not Batman, explicitly) are the large/significant changes he makes and has to go to great lengths to keep subtle or easily dismissed by the public. Reducing something massive and complex to what amounts to a "happy accident" or forgettable coincidence on paper.
Examples:
Buying the Kent Farm. He couldn't buy the house outright, it would draw far too much attention and link his and Clark's identies, even with several steps in between. So Bruce bought the bank, then the Farm.
In Batman Begins, he buys certain gear in bulk to avoid suspicion. He gets thousands/millions of cowl prototype bases because buying ten would be strange.
All of the journalistic manuvering. It's very look here, don't look there. It's artistic. It's sleight of hand with the media. "Brucie falls into a fountain the same night Batman needs to take a night off" no, even better. Bruce, as Brucie, captures attention in a way that doesn't let you even realize that you should be paying attention to something else. He isn't taking away your attention. He has it, and that's the point.
The painstaking and painful steps he takes to fund and oversee the Justice League while maintaining credible distance. The fact that he's able to spin it as CSR without anyone putting the pieces together is impressive.
Tech/behaviors he employs to ensure the government thinks Batman is a low-level vigilante with limited access to complex resources.
Doubling up missions/priorities for events. If he can get intel and a a JL target out of a stuffy Gotham event, he can and will. And on the other side, doubling up patrol/investigations as Batman to benefit Bruce Wayne. None of that intel is a coincidence. Keeping those two lives completely separate only harms him in the long run.
The greatest trick that Bruce Wayne ever pulled was convincing you Batman didn't exist
