Renshaw did his best to earn a national recall, stroking a classy 89 to help steer the Bulls to 4-269 at stumps on Saturday's opening day at Allan Border Field.
Charlie Hemphrey was not out 68 after a 77-run third-wicket stand with Renshaw.
The picturesque ground was forced to host the round-three Shield clash after the Gabba was shut down for US superstar Swift's Tuesday night gig.
But Renshaw had no complaints, savouring the flat deck to find form ahead of Australia's Test series next month against India.
After a double failure in his last match against South Australia, Renshaw took his time to find his feet before exploiting the wicket to hit 11 fours and two sixes.
He saved his most-explosive fireworks for leggie Usman Qadir, at one stage thrashing three-straight boundaries off Pakistan spin bowling great Abdul's son.
Renshaw shared a 90-run opening stand with fellow Test aspirant Joe Burns (49) before he fell short of his 11th first-class ton, trapped in front by Matthew Kelly by a ball that kept low.
It ended Renshaw's knock of almost five hours.
Lanky left-hander Renshaw had hoped to make selectors sit up and take notice with Australian opener Usman Khawaja (knee) under an injury cloud ahead of the first Test against India from December 6 in Adelaide.
Khawaja has undergone surgery and is hopeful of playing Queensland's Shield match against Victoria from November 27 to remain in the Test mix.
After Queensland won the toss, Western Australia finally broke through an hour into the middle session when Burns was caught behind off Jhye Richardson (2-34).
Incumbent Test batsman Marnus Labuschagne lasted only 14 balls before he was caught in the gully for 11 in a blow to his national team aspirations.
The last-placed Bulls are desperate for their first Shield win of the season, returning to Allan Border Field for the first time since claiming the 2017-18 Shield title.
Third-placed WA - captained by Test allrounder Mitch Marsh - have lost Shaun Marsh and Marcus Stoinis to national ODI duties.