Though Bob is an underworld character, what is it that makes it difficult for us to dislike him?

Bob is presented by O. Henry as a likable character on the whole, despite his criminality. He's turned up at the exact location at the exact time he said he would all those years ago. He may be a gangster, a serial criminal, but "Silky" Bob is a man who clearly keeps his promises regarding the things that really matter in life, such as friendship.
There's something rather touching about the way that Bob turns up to the meeting place, hoping to see his old pal after all these years. Among other things, this tells us that Jimmy's friendship really means a lot to Bob, and that's something we instinctively admire, irrespective of what Bob does for a living. And Jimmy greatly appreciates Bob's friendship—so much so that he can't bring himself to arrest his old friend personally.