Bancroft, who was overlooked for Australia's team for the first Test against India, made 72no as WA reached 2-185 at stumps on day three of the pink ball day-night fixture at Adelaide Oval.
SA opener Henry Hunt earlier completed his 10th first-class century, posting 106 as the home side was all out for 253 - a first innings deficit of 120 runs.
Bancroft and WA's first innings centurion Jayden Goodwin (69) then turned the screws, taking the visitors to a lead of 305 runs at stumps.
Bancroft failed to press his Test claims with a wretched run of Shield scores  - 0, 0, 8, 2, 12, 11 and a golden duck.
He also made just 0, 16, 3 and 0 for Australia A against the touring Indians before the Test squad was selected.
But on Monday the 10-Test opener struck three fours and a six in a 206-ball knock.
Joel Paris took 5-34 from 20 overs for Western Australia. (Matt Turner/AAP PHOTOS)
Goodwin, who made a polished 139 in the first dig, continued his fine fixture with a 139-ball innings featuring nine fours before falling to Harry Conway (1-17).
Bancroft and Goodwin put on 132 runs for the second wicket after SA quick Spencer Johnson (1-36) had Sam Fanning caught behind for a second-ball duck.
Earlier, SA's Hunt banked his century and acting skipper Ben Manenti was 73 not out in an innings when Harry Nielsen (49) was the only other batsman to pass 10.
The South Australian struggled to combat WA pacemen Joel Paris, who claimed 5-34 from 20 overs and Jhye Richardson (3-47 from 15 overs).
