We don't know if he was concerned about being picked up by the police. Even if he wasn't concerned about that why would he hang around to wait for a bus that due to what was going on wouldn't probably come for some time.
But while we are on the subject of doing stupid things; why would a guy, who allegedly is on the run, not jump [on] the next bus out of town and instead take a taxi (being willing to give it up for a woman) and then, after a brief visit to his rooming house, walk down to a dead go nowhere street in the middle of a suburban area? That's something no LN have even been able to provide a plausible or believable answer for. What in the world is a guy on the run doing there and why was he in such a hurry to get there?
Which begs an obvious question:
Why was Oswald in such a hurry to leave the Depository in the first place on Nov. 22? And why wasn't he the slightest bit interested in hanging around and seeing what all the commotion was all about?
He had literally a front-row seat for all the "action" surrounding the Book Depository immediately after the President was shot, and what does he want to do? He wants to get the heck out of the area as soon as humanly possible and go to a movie. Not logical at all---unless he's the assassin (or at the very least, he's guilty of being involved in some way in the murder that has just taken place on Elm Street).
Under those latter conditions of guilt, then Oswald's actions (fleeing the TSBD, going to his roominghouse to get his revolver, killing policeman J.D. Tippit, and then ducking into a dark movie theater without paying for the cheap ticket) all make perfect sense to me.
As for Lee Oswald's destination after leaving the TSBD --- We'll never know for certain of course, but some people have speculated that Oswald was on his way to General Walker's house to try and finish the job he failed to complete in April.
It could also be that Oswald didn't have any kind of an "escape plan" at all. Maybe he was just in a mad desperate flight after he made it out of the Depository alive, without any real focus or destination in mind at all. Perhaps he was surprised that he managed to get out of the building alive.
The inner workings of the mindset and thoughts of a Presidential assassin are, indeed, difficult to contemplate and discern. Especially when the authorities only had 48 hours to get any answers out of him.
