After 4.10pm (after first interrogation), according to the late Mr Vincent Bugliosi:
"When they arrive downstairs in the basement holdover room, Sims and Boyd search Oswald—remarkably, no one has yet" (emphasis added).
Even the King of the Warren Gullibles has to boggle at this nonsense!
Even though you haven't spelt it out, you seem to be alleging foul play and if so aren't we left with a logical contradiction, on one hand you are saying that the delay of the Police finding the bus transfer leads to a conspiracy but those same Police are the ones who recorded the times and therefore to cover their tracks could write whatever time they wanted?
I suggest that the delay is most likely linked to assumptions, everybody assumed that someone else searched Oswald therefore no one searched Oswald (too many cooks spoil the broth). And since there was no preconceived wrongdoing they simply listed the correct time.
JohnM