Two options, and a choice between them. Two opportunities to learn more.

She could follow Tucker and witness what happens next, what happens when he goes home with Wash's helmet and without Wash. But she'd only be able to witness that, a passive recipient of knowledge.

...Yeah, screw that, she wants to know what's trying to get out through that door-that-isn't-the-same-door. Besides, that's where the Ghost is looking.

Stacia darts forward and pounds "shave and a haircut" on her side of the door, then waits to see if she gets "two bits" back.