Bruce does not handle being sick well.
It's not that he's a baby about it or anything, obviously. In fact, kind of the opposite? He's just, as ever, very bad at, well... resting. 'Taking a break' doesn't factor into his preferred activities. He can't afford sick days. Bruce Wayne might need a break, but the Bat? He doesn't take breaks. Gotham needs him.
Though he does have at least a surface-level capability of acknowledging when he'd be... less effective in the field. Kind of hard to get the drop on criminals if he's coughing up a lung; kind of hard to stay on top of a situation if fever's making him hazy. He does get that.
It doesn't mean he's happy about it. It doesn't mean he can keep his mind away from work, or stop himself from wanting to head down to the Batcave and at least get something done. It's made him restless, to say the least, and it's not exactly making it easy for him to just stay in bed and rest like everyone keeps telling him he should.
It wouldn't hurt to just go down to the Batcomputer and get some work done, would it? To hear Alfred talk, it would. He's been headed off by a member of the Family every time he's tried to sneak down. Even if he's (probably temporarily) given up on that venture, though, he's still not 'staying in bed' - he's too restless. Awful and exhausted as he feels, he just keeps coming up with reasons to get up.
Which is what finds him making his way to the kitchen now - at least it's nowhere near the cave? He didn't expect to run into anybody at this hour, though (anyone who was around would probably be guarding the Batcave from him), so he does look a bit like a deer in the headlights when he spots you.
"Oh. Uh. I was just... fetching a drink," Bruce says, casually, by way of explanation to your raised eyebrow. A fine excuse - if this weren't the third time today he'd been caught out of bed. And if everyone didn't know full well he could just ring for Alfred and ask for a drink, and stay in his darn bed and rest, because he's sick.