Jimmy obviously must have had mixed feelings about the situation in which he found himself. It would have been a pleasure to see Bob again but painful to realize that he had a duty to arrest him. O. Henry does not identify Jimmy Wells at any time when he is talking to Bob in the doorway of the former restaurant. Therefore the reader knows nothing about Jimmy's feelings during that scene. The reader can surmise what the policeman's feelings must have been in retrospect by remembering what Bob was saying about him at the time.
"But I know Jimmy will meet me here if he's alive, for he always was the truest, stanchest old chap in the world. He'll never forget. I came a thousand miles to stand in this door to-night, and it's worth it if my old partner turns up."
It would be very hard to arrest an old friend after hearing such praise and realizing that he had come all that distance just to see him after all those years. Jimmy may not have made an immediate decision to have Bob arrested after leaving him. But time was of the essence. Bob had told him he would wait there for a half-hour beyond their appointed rendezvous at ten p.m.
The biggest question in Jimmy's mind would have been: Should a policeman who has sworn to uphold the law let a criminal go free just because he happens to be a personal friend? The obvious answer is no. A policeman can and should arrest a wanted criminal even though he can go on liking him.
O. Henry was a master storyteller. He not only created a conflict in Jimmy's heart and mind, but he created what is called "a ticking clock." The character has to make a decision, and he has to do it by a certain deadline because time is running out. O. Henry typically wrote very short stories, so the deadline had to be short in "After Twenty Years." Ironically these men haven't seen each other in twenty years, but Jimmy has only thirty minutes in which to make his decision and make the arrangement he describes in his note to Bob.
"Bob: I was at the appointed place on time. When you struck the match to light your cigar I saw it was the face of the man wanted in Chicago. Somehow I couldn't do it myself, so I went around and got a plain clothes man to do the job. JIMMY."
The most important words in the note are "Somehow I couldn't do it myself." These are the only words from Jimmy Wells that betray how he was feeling while he was talking with his old friend and after they parted. He couldn't make the arrest himself because he was too fond of Bob and Bob was obviously still fond of him. If he hadn't had the time, and if the station house hadn't been close by, he probably would have shirked his duty and let Bob go free. Bob would never have realized that he had been talking to his old friend or that Jimmy had kept the appointment. No doubt Bob would have been disappointed and would have chalked it up as just another instance of the fragility of human friendship. And Jimmy himself would suffer pangs of conscience for a long time afterward because he had failed to do his sworn duty.
O. Henry does not state why Bob was wanted in Chicago. The plain clothes man says that Chicago "wants to have a chat with you." Silky Bob is slick enough to talk his way out of a jam. The reader may end up hoping that Bob is not in serious trouble because that would make Jimmy's betrayal seem less severe.