She had never attacked him or offered any violence towards him in any way. Yet he stalked her throughout the bowels of the ship intent on killing her as she did her best to avoid him and play hamster in the ducting. This has always bugged me as it seems to go against Hulk's established rage nature. What was it about her that pissed him off?
The Hulk on the Helicarrier was not acting just under his own normal personality. He was also being manipulated by Loki into destroying the Avengers. This is what Natasha figures out after her interrogation of Loki, and what everyone else figures out when they see Bruce Banner picking up Loki's staff.
When Bruce and Natasha are both injured in the explosion and Banner transforms, Natasha is the first person he sees, and his anger is now completely out of control. Thus, he focuses on her as the most readily available target and chases after her.
Note that, once more attractive targets start presenting themselves, he leaves off Black Widow and goes after Thor, then the fighter jet, just as you'd expect.