Bader, yet to win a title in 13 seasons on the Tour, shot a four-under 68 to edge ahead of world number one Yani Tseng, who finished the opening round a shot back.
American Bader, 38, had three birdies to reach five-under but blotted her copybook slightly with a bogey on the par-4 ninth.
Tseng, who has won three of the first six tournaments on this season's calendar, was second alongside Angela Stanford, Jiyai Shin and Brittany Lang.
Of the chasing pack, Sun Young Yoo was the best after shooting a 70 while I.K. Kim, still recovering from her miss from one foot on the final hole of the Kraft Nabisco Championship, hit a 71.
Michelle Wie, who has struggled badly in her last two starts, was 10 strokes back.