Disclaimer: Don't own.
What is this I don't even.
Bruce Wayne was a well-known figure in the right circles. Known as the Batman to his colleagues, he was relatively infamous due to his obsessive tendencies. As one person put it, there were zoologists and there were zoologists, and Bruce Wayne was the latter. But they put up with him, because he was a genius (his work on white nose syndrome was renowned) and because they understood that he wasn't quite right in the head. Having your parents murdered in front of you at a young age would do that to anyone, though no one quite understood why that led the Wayne heir to seek a career in zoology and cultivate an obsession with bats.
It was generally accepted that other than his proteges the only people who would put up with Bruce Wayne on a regular basis were the environmentalist Clark Kent and the anthropologist Diana Prince, though even they had their limits. They were the ones who dragged Bruce to scientific conventions, urged him to publish his findings, and got him to interact with creatures that weren't bats. Not that they weren't a little infamous themselves; after a few too many overambitious ideas Clark earned the mocking title Superman, while Diana was known as Wonder Woman, after her favorite remark towards every new thing that crossed her desk: "It's a wonder!"
Dick Grayson, Bruce's first protege, was much more accepted among the scientific community than his mentor. He was well respected, everyone hanging onto his every word. He was popular and liked, practically getting research grants thrown at him. But no matter what their accolades, his loyalty was still to the Batman.
Everyone had been hoping that his second protege, Jason Todd, would turn out like Dick. They really didn't need another Batman on their hands. Unfortunately, neither happened. He was involved in a tragic scuba diving accident whilst studying clown fish, and his death pushed Bruce over the edge. He drew into his obsession, his temper shortened, and most sane people cowered in fear for a time.
When Dick convinced him to take on a new protege, everyone worried for the boy. But it turned out they needn't fear; if anything, Tim Drake had a calming effect on the Batman. He was Bruce, only without the bat addiction. When he suffered a series of personal losses, each soon after the other, everyone worried that he would become like his mentor, but Tim overcame it and successfully graduated from the shadow of the Batman.
Eventually of course it had to come out that Bruce Wayne had a son with Talia, the daughter of mass industrialist Ra's al Ghul. Ra's al Ghul was not exactly known for his environmental policies, rivaled in that fact only by Lex Luthor. (Clark Kent, who had long since considered the two of them Most Wanted for crimes against the environment, temporarily stopped talking to Bruce.) Damian was rude, brash, and arrogant, and once enough of the scientific community had met him they came to the group conclusion that he would be the one to blow up the planet. The only thing standing between Damian and the end of the world was the Batman, and they did not find the thought comforting. Everyone was happy when Dick intervened but eventually he had to go back to his own life, and physicist Oliver Queen had a few choice words about being trapped between opposing forces to describe the situation Damian was in. Or, as chemist Barry Allen put it, "It's like a game of pong where the ball just starts going faster and faster. Eventually someone's going to lose badly, and the winner's going to feel so good about it that they're going to take a shit on them right then and there."
Dick had faith in Damian, but it was quite possible that he was the only one. Bruce certainly didn't, and neither did Dick's on-again off-again girlfriend Barbara Gordon. The daughter of one of Bruce's old college professors, Barbara assisted Bruce and Dick with their research until a horrible caving accident cost her the use of her legs. It was at that point she decided that she wasn't interested in nature to the extent that Bruce and Dick were, and changed her focus to computer programming and technology innovation. She agreed with most of the scientific community that Damian was a little terror. Damian did bond with Selina Kyle, an expert on big cats, but even she thought that his grandfather's hold on him was too strong.
But Bruce Wayne, zoologist, didn't care about any of this at all. He didn't care that Clark and Diana were the only two who put up with him. He didn't care what his peers thought of him or his proteges. All he cared about were bats. And that was why he was the Batman.