In such a fanfiction, they might start by sizing each other up. Bruce would be intrigued by Tony's high - tech gadgets and playboy lifestyle, while Tony would be curious about Bruce's dual identity and his more brooding nature. They could end up collaborating on a project, perhaps something to do with improving Gotham's infrastructure using Stark technology.
Well, in a Bruce Wayne meets Tony Stark fanfiction, there could be a lot of clashes at first. They both are used to being in charge and having their own ways of doing things. But eventually, they might find common ground in their intelligence and drive to protect. Maybe they would team up to take on a common enemy that threatens both Gotham and the world at large. Bruce's combat skills and Tony's technological prowess would make for an interesting combination.