"Can I take you home, or?" He's not being deliberately obtuse - he genuinely doesn't know if making such a suggestion would be perceived as being-- patronising or whatever. Of course he's not going to make Arthur limp home, but he's not sure if he's supposed to stand around waiting until Arthur has felt like he's proven whatever it is he feels the need to prove and keels over in pain, exhaustion, frustration, some combination of the three, or if he's allowed to suggest that maybe it's not such a great idea to keep going.

"I haven't--... I've been living under a rock, alone, for eighty years." Would it be funnier if he faked a laugh or if he just left it like that with his deadpan delivery? "This would be easier if you just. Told me what you want me to do." Waiting for Bucky to learn how to pick up on all these social cues, one would be waiting a very long time.