Maybe Mary Bledsoe was not on the bus but Oswald was.

Some have used serious flaws in Mary Bledsoe's testimony as part of an argument that Oswald was not actually on the bus but perjured testimony from McWatters and Bledsoe was used to construct a fleeing assassin scenario to explain Oswald's being on the bus.  I think the serious flaw in this argument is that it doesn't make Oswald look like a fleeing assassin but really more the opposite.  Consider that maybe McWatter's was telling the truth, Oswald was on the bus, but Mary was not.  Mary seemed unsure about a great many things but one thing she was definite about was that Oswald did not get off the bus when the man stepped in and said the President had been shot.  She was sure Oswald got off later even though she also said she was trying not to look at him the whole time he was on the bus.  Mary's testimony accomplishes two things.  It refutes McWatter's testimony about the timing of Oswald's departure and it gives Oswald a reason to have gotten off the bus other than hearing the President had been shot.  She knew him by name and he didn't know how long it would be before his name would be spoken.  I mean that was the story that would be told and not the actual situation.   The preference was that no story would be told because nobody would notice that Oswald got off the bus right after hearing that the President had been shot.  When people are covering up, they sometimes think something is going to give everything away because they know how things are connected.  In reality, they aren't obvious at all and sometimes trying to hide them is what blows the cover up.  I think those covering up were very concerned that Oswald getting off the bus right after hearing the President had been shot could be very revelatory.