If you're willing to believe that he showed up for duty in Alabama, yet no one there remembers this future president of the United States...
...then let's take a look at this excerpt from the Texas Military Code.:
Acts 1987, 70th Leg., ch. 147, § 1, eff. Sept. 1, 1987. § 432.130. Desertion
(a) A member of the state military forces is guilty of desertion if the member:
(1) without authority goes or remains absent from his unit, organization, or place of duty with intent to remain away permanently;
(2) quits his unit, organization, or place of duty with intent to avoid hazardous duty or to shirk important service; or
(3) without being regularly separated from one of the state military forces, enlists or accepts an appointment in the same or another of the state military forces, or in one of the armed forces of the United States, without fully disclosing the fact that he has not been regularly separated. (b) A commissioned officer of the state military forces who, after tender of his resignation and before notice of its acceptance, quits his post or proper duties without leave and with intent to remain away permanently is guilty of desertion.
(c) A person found guilty of desertion or attempt to desert shall be punished as a court-martial directs.
As is evident from the above, one of the elements of desertion is intent to remain away permanently. Bush asked for discharge from the TANG on September 5, 1973, and apparently left for grad school immediately after. (Does anyone know of university grad school years starting after September?) Now, let's take another look at that excerpt from the Texas Military Code.
(b) A commissioned officer of the state military forces who, after tender of his resignation and before notice of its acceptance, quits his post or proper duties without leave and with intent to remain away permanently is guilty of desertion.
So... On September 5th, 1973, George Bush asked for discharge (resigned from) the Texas Air National Guard, thereby stating his intent to not return to duty with the TANG. Now let us examine another document
That document is Bush's Discharge from the TANG. Notice block 33, at the bottom: "NOT AVAILABLE FOR SIGNATURE". There it is, folks. Bush left Texas before his resignation from the TANG was approved. There is your evidence of desertion.
Thanks, Hank!