Well you can take the man out of the mission but you can't take the mission out of the man. He doesn't know exactly where all Arthur's haunts are but he starts at the house since that made the most sense.

Where most people would have rocked on up there and banged on the door, Bucky makes two non-identical rounds around the property, checking out the immediate neighbours, if anything is amiss about the house. He couldn't read any immediate distress in the message but he has to assure himself more than anything that Arthur doesn't need immediate violent intervention.

Only when he's sure that there's no signs of forced entry or anybody watching them or anything like that, does he circle around the back of the house and send his reply:

back door