Shaw held the distinction of being the first African-American bishop of the Methodist Church (at the age of 71) to preside full-time over a predominantly white Annual Conference: the Southern California-Arizona Conference (in 1950, coincidentally the 100th annual meeting of this body), which met that year at the University of Redlands.
He was the eighth of eleven children of the Reverend Duncan Preston and Maria (née Petty) Shaw.
They had children Alexander Preston Jr., Bernard Johnson, twins Lena Anita and Bessie Elaine, Helen Marguerite, and Wilbur Allen.
Reverend Shaw distinguished himself as a pastor serving the following appointments: Westminster, Maryland (1908–09); Harrisburg, Pennsylvania (1909–11); Winchester, Virginia (1911–15); Little Rock, Arkansas (1915-17); and the Wesley Chapel Methodist Church in Los Angeles (1917–31).
Shaw also distinguished himself as the elected editor of the Southwestern Christian Advocate, an important periodical of his denomination.
When he solved this problem by persuading his congregation to rent him another house, while leasing the parsonage "to a much shorter man", newspapers in the Washington and New York areas delightedly picked up the story, causing the Reverend Shaw "a good deal of embarrassment".
Reportedly, he would occasionally bring an outstanding boy or girl into the pulpit with him, to lecture on how the church could be made even more interesting to young people.
Shaw was also reported by Time magazine as "consistently advocat[ing] self-improvement and development for his race."
Shaw held that "a sufficient amount of real excellence – as has been achieved by Marian Anderson and Dr.
Above all, said Time, "[Bishop Shaw] believe[s] that Negroes should observe the rule he himself has followed with such conspicuous success: take on responsibilities."
He was, however, called out of retirement in 1953 to again serve part of the New Orleans Area following the death of Bishop Robert Nathaniel Brooks.