The opener-keeper had 161 runs to his name by the end of play on Monday.
And he reached his double century shortly before lunch on day two after taking spinner Travis Head to the cleaners with a series of boundaries.
Bancroft's 513-minute, 351-ball innings featured 22 fours and three sixes.
The 24-year-old has now produced scores of 76no, 86, and 228no in his past three Shield innings, with his hot form firmly thrusting him into the selection frame for the Ashes opener at the Gabba, starting November 23.
In reply, the Redbacks ended day two at 6-322, with Jake Weatherald (152 off 180 balls) the star of their innings.
Young WA paceman David Moody claimed three wickets including putting a stop to Weatherald's session.
Debutant Andrew Holder claimed his maiden Shield scalp when Tom Cooper was caught at mid wicket by Jhye Richardson.
Redbacks batsman Jake Lehmann lasted just 16 balls before he edged Richardson to slip.
South Australia duo Alex Carey (26no) and Joe Mennie (21no) will resume on Wednesday.