The newspaper said that the then Speaker of the Texas legislature, Ben Barnes, asked the chief of the Texas Air National Guard, Brigadier General James Rose, to have Mr Bush Jnr accepted into the Guard's pilot training programme, a common draft-avoidance route for the well-connected.
While there have been persistent reports that patronage helped Mr Bush Jnr, who is now governor of Texas, to avoid the draft, this is the first time that a reporter has supplied anything like chapter and verse. According to the Post, Mr Barnes intervened on Mr Bush's behalf sometime in late 1967 or 1968 at the request of Sidney Adger, a Houston businessman and a friend of George Bush Snr, who was then a Republican congressman for the city.
The Post implicitly concedes that establishing a direct request from Mr Bush Snr will be hard. Both George Bushes - father and son - have denied any intent to dodge the draft, and George Bush Jnr said he "wanted to be a pilot", met the requirements, applied and was accepted in the normal way. Two of the main players - Mr Adger and Brigadier General Rose - are dead.
None the less, the timing of Mr Bush Jnr's acceptance into the Air National Guard, two weeks before he graduated from Yale, at a time when the service was highly competitive, suggests a measure of special treatment.
What is more, Mr Barnes - who allegedly made the key link - is still alive and said in an interview earlier this year that he was sometimes approached to help influential people to obtain National Guard positions for their relatives and friends. While he denied receiving such a request from any member of the Bush family, he would not comment on whether there had been an indirect request. This is what the Post alleges, suggesting a bargain transacted in nods and winks among associates.
The newspaper also establishes that Mr Bush Jnr contacted the Texas National Guard during the winter vacation of his final year at Yale to find out "what it took to apply". And it quotes the late Brigadier General Rose as telling a friend: "I got that Republican Congressman's son from Houston into the Guard."
The issue could be elucidated further next week when Mr Barnes is summonsed to testify in a lawsuit brought by the aggrieved former director of the Texas state lottery, who is contesting his dismissal. Among his claims is the charge that Mr Barnes was complicit in a deal to keep secret the facts of Mr Bush Jnr's admission into the National Guard.
Whether the accusation could scupper Mr Bush Jnr's, chances of winning the presidency is highly doubtful. Bill Clinton demonstrated that such a history need not be fatal to an aspiring president. The saga does, however, add to the impression of Mr Bush Jnr as a child of privilege and patronage, which could tell against him.
As the son of a former president, he has been able to capitalise on his father's associates for his prodigious fund-raising efforts, and for illustrious advisers. Both parents have defended their son against allegations that he used cocaine in his twenties and supported his refusal to answer questions on the subject. Such solidarity may not be an advantage: Bush- detractors have already dubbed him "Bush-baby", a name that could just stick.