Thanks for the question.
I assume that you are referring to the former first lady rather than the daughter of the President. It is highly improbable that Aleister Crowley ever met her mother let alone had an affair.
Barbara Bush was born Barbara Pierce. Barbara Pierce was the third child of the former Pauline Robinson (1896-1949) and her husband, Marvin Pierce (1893-1969), who later became president of McCall Corporation, the publisher of the popular women's magazines Redbook and McCall's. She was born and raised in the suburban town of Rye, New York, near New York City and went to Rye Country Day School, followed by boarding school at Ashley Hall in Charleston, South Carolina. President Franklin Pierce was an ancestor.
Pauline Pierce was born Pauline Robinson. W magazine (no relation to the current President) once described her as "beautiful, fabulous, critical, and meddling" and "a former beauty from Ohio with extravagant tastes".
Rumors that Pauline had an affair with Dwight D. Eisenhower have never been verified, nor is there any evidence that she ever even met the WWII commander. By many personal accounts, she was a faithful wife and loving mother. Still, gossip tabloids from the '40s often associated her with prominent men in politics and film. However, Barbara Bush was born in 1925 and married in 1945 so there is no possible connection.
Aleister Crowley was in Sicily at the time. Crowley, along with Leah Hirsig, founded the Abbey of Thelema in Cefalu, Sicily in 1920. The name was borrowed from Rabelais's satire Gargantua, where the "Abbey of Theleme" is described as a sort of anti-monestary where the lives of the inhabitants were "spent not in laws, statutes, or rules, but according to their own free will and pleasure." This idealistic utopia was to be the model of Crowley's commune, while also being a type of magical school, giving it the designation "Collegium ad Spiritum Sanctum", The College of the Holy Spirit. The general programme was in line with the A∴A∴ course of training, and included daily adorations to the sun, a study of Crowley's writings, regular yogic and ritual practices (which were to be recorded), as well as general domestic labor. The object, naturally, was for students to devote themselves to the Great Work of discovering and manifesting their True Wills. By this stage, he was known as the wickedest man in the world
Crowley died in 1947 a bankrupt shunned by society and addicted to opium.
Regards