On the same day that Matt Renshaw and Marcus Harris both failed in their respective Shield matches, Bancroft struck a steady 57 on day one in Adelaide.
With Western Australia all out late in the day, South Australia went to stumps at 0-27 with an early advantage in the fixture.
Wes Agar was earlier the star with the ball for the Redbacks, claiming career-best figures of 6-42 to rip through the visitors' middle and lower order.
But it was Bancroft who keeps knocking on the door of national selectors.
Patient early, the opener hit Nathan McAndrew for two boundaries in the over before lunch before he was caught behind pushing at one outside off stump from Agar.
With David Warner set to retire after the SCG Test against Pakistan in January, it is Bancroft who has made the loudest statement to take his spot for the rest of the summer.
He began the Shield season with 122 against Victoria in Perth, before backing it up with 91 against Tasmania.
Harris, who has long been viewed as next in line by Australia's selectors, was handed a national contract earlier this year and taken as a back-up batsman on the Ashes.
But Victoria's opener has started the season poorly, with Thursday's first-ball duck against NSW coming after scores of 0 and 10 in his other Shield match against Queensland.
Renshaw scored seven on Thursday against Tasmania, after scores of 17, 55 and 135 to start the season.
Bancroft's innings took him past 6000 first-class runs for Western Australia, making him the 12th player to do so.
The opener's runs also made him the top scorer for WA, who had several batters make starts without going on.
Sam Whiteman scored 30 at the top in a 43-run stand with Bancroft, while Teague Wylie faced his first 25 balls without scoring before being caught behind for 22.
Hilton Cartwright hit 56 after overcoming a painful blow to the knee, but was caught in the deep trying to take on Ben Manenti as part of a late-innings collapse of 7-71.
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