He gives her a little time after he realizes she's not anywhere he's used to looking. He keeps an eye out, and he asks JARVIS to tell him if she's in danger, but he doesn't actually go searching for her. As much as he hates letting her out of his sight... he's trying.

It doesn't end up being much time at all before he really starts looking, but it's the thought that counts?

It's a little longer before he finds her, and when he does he's careful to let her hear him coming. Not that he thinks she wouldn't notice, but just in case she's distracted.

"Tasha," he says quietly, when he's only a couple of feet away, close enough that he can reach out a hand and brush his fingers against her arm.