Bruce feared letting himself get too close.
Not just because of you; if you became a weakness of his, he'd be putting your life at risk. It would cloud his judgement and make him do irrational things. It might be a life so sweet, and so tempting, that it distracts him from his work as the Knight, causing a plethora of collateral damage, all because he couldn't resist you. Some part of it was agonising - infuriating. That he may have to accept that something like love could never be a part of his life. That he was so shackled by his duty and the possibilities of everything that could go wrong, that it didn't leave him any room to consider that it may possibly go right. How will he ever know for sure? He's too frightened to take that risk. Maybe a part of him wishes to punish himself and strangle a love that could make him happy. That would make him happy.
But the two of you work together, and pushing you away isn't an option. Keeping things strictly professional was his goal; it was a difficult challenge, Bruce wouldn't lie about that. But his facade wasn't one so easily cracked, and it would remain that way, even for you. For the most part.
It came in the form of little things. He would often leave a cup of coffee for you in the Batcave when he knew you would be there, or when they had a big case to work together. It would always be your favourite, having memorised it the first time you had told him, and making sure Alfred prepared food you liked for your arrival. The old butler often made snide comments, pushing the two of you together, yet Bruce would shut it down. In fear? Probably. You were nothing alike; the sunshine to his darkness.
Bruce approached you, his suit on but cowl off, his footsteps tentative and silent against the floor. Hours of working on a case had led the two of you to hit a mental roadblock, and he wanted to make you feel better.
"Spar?" He offered gruffly, terse, gesturing to the arena with a small incline of his head. "Might clear our heads. You look like you need a break."