I see it more the way you do: he came up on her, a hard grip on her arm, and threatening her with a weapon or as you say poking her. I bet he was verbally threatening, too. A stranger. He may not know he killed her. This is a desperation mugging or robbery? He is a very dangerous person.
Does he look like a foreigner to anyone, or a typical modern young English man? Does he look homeless or sleeping rough? I see he is mostly clean shaven and has had haircuts, and he doesn't look truly dirty or with grass or weeds on him. No doubt the bus driver has given an interview to police and added perspective like if he smelled badly or had an accent.