Clint had lost sight of Hulk for a few hours. Part of him had been hoping Hardy would have gotten the giant green guy to calm down but he also hadn't been holding his breath. After all, this wasn't the Hulk she was familiar with so her calming tactics had a chance of not working but the archer had kept quiet on it. After all, if it worked, it worked.
So while he searched for trails of the Hulk (which wasn't hard to find and follow for a sniper), he had sent a message on the boards to see if Banner was back yet. And lo and behold, so not the case. Still, Clint didn't care either way. While he wasn't too aware of just how intelligent the Hulk was, the big guy was smart enough to have helped them out in smashing up Loki's army and to have saved Stark. So there was more going on with the Hulk than anyone knew.
Arriving at the quarry, Clint peered through his scope and caught sight of green. He stayed hidden for a while before he decided to go keep Hulk company. Teammates or friends, they were allies all the same and Clint honestly wanted to get to know this side of Banner better.
So, perhaps a bit unwisely, he headed over to the larger being, making some noise and being visible so Hulk wouldn't freak out and smash him. When he was several meters away he stopped, his bow slung over his shoulder and everything about him as unthreatening as possible.