As for if Bates killed Green or not, circumstance might look bad again for him, but I still do not think he did it. He may say aloud that he wants to kill Green and feel in his heart that he wants to, but he and Anna would have everything to lose if he does. Mrs. Hughes told Bates how much Anna loves him and that him going away, either leaving her as he was planning since he thought she no longer loved him (or another trial and prison) would be too much for her. Anna asked him to "brood" on her and not what had happened to her. I am hoping that is what he has been doing. Bates now knows it was Green but also sees his wife struggling to try to keep it a secret. He is not stupid, he has to have figured out that she is doing all this to try to keep him safe and with her, that he means that much to her. Bates has to be struggling too because he loves Anna and feels guilty that he did not protect her and that he, as her husband, should do something. I could be wrong, but I think Bates hired a detective in York to try to get some damaging evidence against Green. Green was an arrogant scumbag, surely there were other victims, other crimes. It has to be torture for Anna, fearful that Bates will seek revenge. But, it would also be hard on Bates who would not want Anna to know or worry that he is going after Green in another way and spending money in the process. As for the train ticket there was no date on it and it was from York to London and not Downton to London. It could be that it was an expense the detective incurred and gave it to Bates, possibly with other bills, to be reimbursed. Lastly, if Bates were to confront Green, I think it would have been face-to-face, man-to-man, and he would have wanted Green to know it was him. I do not see him tripping or pushing someone from behind, there is little honor in that and Bates lives by his code of honor, that is more something someone like O'Brien would do. Green could have simply tripped. Or perhaps he did trip while trying to get away from someone, if it was the latter, I think it was a detective or another victim. Time will hopefully tell. But, in the end, I think it will prove that in all of this, both Bates and Anna were trying to do what was always best for the other.