Darcy saw the sign in the elevator on the way down to try to train (or, more accurately, watch other people train and listen to music while realizing how totally outmatched she is in the Arena). And the idea of having her own pet Tribble is actually super cute. It's while she watches Bucky train that something hits her: yeah, having her own pet Tribble would be great, but Bucky having one to try to lessen his crazy high intensity could be even better.

She would interrupt him, but that seems like a terrible idea based on past experience. Instead she waits until he's done and follows him to the elevator, blocking him when he tries to press the button to his floor. "Nuh-uh, we're going on a little field trip."