Batman saw the Joker run inside, but that had probably been intentional. Batman knew the odds were high that he was running into a trap, but there was little else he could do. He just had to count on his survival instincts. He ran inside the building after the Joker, not surprised to find himself in a maze. There was little the Joker could do to surprise him. The man was insane, and 'Expect the Unexpected' definitely applied.
Batman ran down the dusty corridors, trying to work the maze by instinct. There was a logic to all mazes, even the Joker's. He just had to find it. When the dust made him cough, he reached down to his belt and pulled a small filter-based gasmask from his belt and attached it to his cowl, over his nose and mouth.