The man standing in the doorway is the picture of success and self-confidence. He is not the least bit nervous when confronted by a uniformed policeman. We do not know that he is crooked until we reach the end of the story. He could have been involved in various business enterprises in what he calls the West (which we would not call the Midwest). Of course, he could hardly brag to a policeman about what sorts of shady deals he might have been involved in.
It may seem unusual that Bob should have come all the way from Chicago to New York to keep an promise he made twenty years earlier. But O. Henry needed to establish that Bob felt perfectly at ease even while talking to a police officer and even though he must have known he was wanted by the law. By distancing him from Chicago approximately one thousand miles, O. Henry makes it seem plausible that Bob would have no fears of being apprehended. Furthermore, O. Henry distances Bob from New York by twenty years--so there is a great deal of distancing in this story to explain why Bob is so calm, cool and collected. It is only because O. Henry wants to account for a wanted man's total self-assurance that he arranges to have him travel a thousand miles to meet an old friend and specifies that the dinner date was made twenty years earlier. Why would a man travel a thousand miles on an old-fashioned steam-driven train just to have dinner? It is hard to believe--but O. Henry was forced to put it in. He wants Bob to feel at ease so that he will confide in a cop and thereby provide almost all the essential exposition.
Bob is supposed to be a smooth customer, and he knows he is wanted by the law. He should know better to confide in a copper. He certainly wouldn't be so talkative with a Chicago cop! He is not as smart as he thinks he is. Maybe O. Henry, who was a New Yorker, wanted to show that a man like Bob might be considered slick in Chicago but not in New York. Bob is a big-time operator in the "West" but a small-timer in New York.
In the note the plain clothes man hands Bob at the very end of the story, Jimmy writes:
When you struck the match to light your cigar I saw it was the face of the man wanted in Chicago.
Before giving him Jimmy's note, the plain clothes detective says:
"You've been under arrest for ten minutes, 'Silky' Bob. Chicago thinks you may have dropped over our way and wires us she wants to have a chat with you."
How could Jimmy have seen that Bob had "the face of the man wanted in Chicago"? It was not possible to send a picture by wire in those days. O. Henry never mentions Bob's last name and only calls him "Silky" Bob one time, right at the end. O. Henry had a plot problem which he simply ignored. The Chicago police could have sent out wanted flyers, but these flyers might have only contained Bob's name and general description and not his picture. Did Chicago have a picture? Did they know his full name?
O. Henry has to specify that Jimmy happens to have a beat that includes the hardware store where Bob is waiting. Otherwise Bob would have brains enough to become alarmed if a uniformed cop suddenly came up to him out of nowhere. He sees the cop trying doors and twirling his club and naturally assumes, as does the reader, that this is just a cop on his beat.