At stumps the visitors were 7-255 after Cameron Green and Jhye Richardson helped WA recover from a middle-order collapse with an unbroken 84-run stand.
Green was not out 50 - his maiden first-class half-century - and Richardson unbeaten on 35.
The pair showcased some remarkable cricket shots which included 12 fours between them.
After the Bulls won the toss, WA recovered from 2-2 in the third over to be cruising at 2-120 prior to tea.
Marsh shared a 118-run third-wicket stand with Marcus Stoinis (44) before the Bulls hit back with the ball.
The veteran was finally caught at bat-pad which ended an impressive 167-ball knock that lasted almost four hours and included 13 boundaries.
Josh Philippe (22) and Hilton Cartwright (20) provided brief cameos in the middle order which helped push WA's total towards 200.
WA will resume their first innings when day two gets underway from 8:00am AWST tomorrow.