Bucky would be slightly hesitant with Kit coming along but then would just figure he could keep a close eye on her. Plus those hypnotism abilities could come in handy.

He'd keep her bag in mind if they found anything particularly useful, too, or if they needed to bring any tools or anything. He has a bag of holding himself so he'd probably just use his but the more space the better. More stuff is always better when it doesn't mean more weight to have to carry.