The Secret Service and the FBI reconstructed Oswald's steps (with the help of Cecil McWatters and William Whaley) in an attempt to determine the absolute earliest that Oswald could have reached the rooming house.
Based on McWatters' statement of where it was that Oswald boarded the bus (we know Oswald boarded that bus because he had McWatters' specific bus transfer and McWatters said he issued that transfer to only one woman and only one man), Oswald walked about seven blocks east (into the downtown area) after he left the Depository within three minutes of the shooting.
"So I gave her a transfer and opened the door and she was going out the gentleman I had picked up about two blocks (back) asked for a transfer and got off at the same place in the middle of the block where the lady did. It was the intersection near Lamar Street, it was near Poydras and Lamar Street." -- Cecil McWatters
They concluded, based on what McWatters told them (along with the Secret Service agents and FBI agents walking the route in an average time of six and a half minutes), that Oswald boarded the bus around 12:40 near the intersection of Field St. and Elm St. and then, after being on the bus for no more than four minutes, Oswald got off the bus near Lamar St. and Elm St. (asking for the transfer as he got off the bus).
So now we have Oswald leaving the bus around 12:44.
Oswald then walked three to four short blocks to the Greyhound station where he boarded Whaley's cab. This has Oswald entering the cab around 12:48.
They then, with Whaley, reconstructed the cab ride from the Greyhound to the intersection of Beckley and Neely (Oswald got out of the cab on Beckley just north of the intersection with Neely). They concluded (using a stopwatch) that the cab ride took five minutes and thirty seconds.
So now we have Oswald exiting Whaley's cab on Beckley at 12:53-12:54.
Still using the stopwatch, they concluded that it was a five minute and forty-five second walk from the point Oswald exited the cab back to the rooming house.
I think Oswald got to the rooming house between 12:58 and 1:00 and was back in his room just long enough to grab a jacket before hurrying out the door, zipping up a jacket as he went out the door.