In my "Oak Cliff Time Trials" thread, regarding where Oswald may have been heading when he left the rooming house and what he may have been thinking, I speculate that Oswald was trying to get to the bus stop outside of the Jefferson Branch Library at Jefferson and Marsalis. I state that Oswald's transfer was good at that bus stop at Jefferson & Marsalis until 1:15 and if the transfer was for a bus line where a bus stopped there only once per hour, then the transfer would be good for the next available bus.
Quoting "With Malice", I also state in the "Oak Cliff Time Trials" thread that Oswald could have caught the Lancaster Road bus at that bus stop at 1:30 which would have taken Oswald south from that bus stop to Greyhound bus connections through Laredo, TX and on to Mexico.
Regarding Oswald's motivations and actions once he walked out the front door of the rooming house, I have researched this stuff for years having always been curious about what could have been in Oswald's mind and what his destination may have been. I worked closely with Frank Badalson and Dale Myers through phone calls and Skype sessions in order to post the best accurate information when preparing the "Oak Cliff Time Trials" thread.
Along with the tedious read that was the Warren Commission testimony of bus driver Cecil McWatters (which I read in full for the first time almost twenty years ago), I have read the David Belin papers pertaining to J. Lee Rankin's April '64 request to the U.S. Secret Service for bus route information relative to bus travel from Dallas to Mexico.
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Regarding the bus transfer:
"The transfer normally given by the bus line is valid for 15 minutes. If the buses to which the transfer is being made are scheduled an hour apart, the transfer would be good for the next bus, regardless of the length of time from leaving the bus from which the transfer ticket was obtained. The transfer would be valid anywhere along the route of the bus from which the ticket was received, and could be used at any routed bus crossing that particular bus line, i.e. if an individual rode on bus route A obtained a transfer therefrom, the individual could conceivably transfer to bus line B at any point along the route of bus line A, provided the transfer be used within 15 minutes of the time of issue or upon the next scheduled bus after the time of issue."
They also determined that the Lancaster Road bus stopped at the bus stop at Jefferson & Marsalis (city bus stops were used by various city bus lines).
To simplify it, let's say bus route A is the Marsalis line which obviously travels down Marsalis Avenue. Let's say bus route B is the Lancaster Road bus. Since both buses use the bus stop at Jefferson and Marsalis, this means that if one has a transfer for the Marsalis line, he could transfer to the Lancaster bus. This Lancaster Road bus would take Oswald south from that bus stop to Greyhound bus connections through Laredo, TX and on to Mexico (more on that in a moment).
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J. Lee Rankin (General Counsel, Warren Commission) asked the United States Secret Service to provide information on bus travel from Dallas to Mexico. Secret Service agents interviewed Mr. McFadden, Terminal manager, Greyhound bus depot, Dallas, TX.
"During the period in question, all buses traveling to the Mexican border would stop between terminals to pick up passengers both in cities and on the open highway. This stop would be contingent on traffic regulations and safety procedures. The passengers could then purchase their ticket on the bus."
Oswald had $13.87 on him when he was arrested. One could get from Dallas to Laredo for $12.80.
David Belin called Forrest Sorrels, Secret Service Special Agent In Charge of the Dallas office and requested information of bus routes and taxi routes in the Jefferson-Marsalis area.
Belin wanted to know if the Greyhound, Continental or City bus lines could be flagged anywhere along the route. The answer:
"The City bus lines have designated bus stops and can only be boarded at these bus stops. The Continental and Greyhound bus lines can be flagged by any persons anywhere along the route; these lines will stop and pick these persons up. The ticket is then purchased on the bus for cash."
Belin wanted to know what bus routes could be boarded at the bus stop at Jefferson & Marsalis:
"The Marsalis bus route, which travels from the downtown Dallas area to the Singing Hills residential area in Oak Cliff, Dallas; The Sunset Hampton bus route which travels south on Jefferson to Hampton Road, then returns to Dallas as the Lagow and Second bus travels north on Jefferson to the downtown area. -- Lancaster bus, begins at Kingsley Avenue and travels north on Lancaster making a stop at the Veterans Administration Hospital."
Belin also wanted to know what is the route of the Greyhound bus line stopping at the Lisbon Flag stop:
"The Lisbon Flag stop is a designation for a stop for Greyhound buses at the Veterans Administration Hospital, which is located on Lancaster Road. The bus travels from the downtown area across the Corinth Street Viaduct to Corinth Street; down Corinth Street to Lancaster; and then down Lancaster to the Veterans Administration Hospital."
"The Greyhound bus line will pick up any passengers upon being flagged anywhere along their route provided it is safe to stop on the highway or streets."
If you read what I am spelling out above, from the bus stop at Jefferson & Marsalis, one could catch the Lancaster bus and take it south to the Veterans Administration Hospital. Then from the hospital, one could board the Greyhound bus which would take one to the border at Laredo, TX.
Have a look at the David Belin papers regarding City and Greyhound bus routes between Dallas and Mexico:
https://www.fordlibrarymuseum.gov/sites/default/files/pdf_documents/library/document/0393/23811296.pdf