Resuming on 263, Bangladesh saw the CA XI post 355, thanks to a superb 130 from Teague Wyllie, who shared a 167-run sixth-wicket stand with Jake Doran (76) after the hosts had slipped to 139 for 5. Captain Kurtis Patterson also contributed 53.
Fast bowler Hasan Mahmud was Bangladesh's standout performer with 4 for 42, while Mehidy Hasan Miraz, who scored an unbeaten century on the opening day, chipped in with 2 wickets.
Bangladesh's reply got off to a poor start as Campbell Thompson dismissed both Shadman Islam and Mominul Haque, leaving the tourists reeling at 19 for 2 at stumps, still 73 runs behind.
With only Najmul Hossain Shanto's 37 and Miraz's century among the top-order contributions so far, Bangladesh's batters will be looking for valuable time in the middle on the final day ahead of the opening Test against Australia.
Meanwhile, Taijul Islam sustained a finger injury while batting against the Cricket Australia XI as he has been advised to rest after receiving a bandage on the injured finger.
Bangladesh national team physiotherapist Bayezidul Islam confirmed the development.
