Marcus Harris, a fellow contender for the vacant opening spot, also failed to capitalise after he made a start on day one against India A in Mackay before falling for 17.
The adopted Victorian, who last played a Test in January 2022, was given a life just after tea when he was dropped at third slip.
But the left-hander fell shortly after by half playing a shot and was removed by India A seamer Prasidh Krishna.
Australia A captain Nathan McSweeney, who bats at No.3 for South Australia and is another contender to fill the Test opening void, has a chance to press his case after coming in to bat at No.4.
After India A were rolled for 107 batting first in Mackay, NSW teenager Konstas lasted just three balls in his first audition for Test honours.
Konstas had a stunning start to the Sheffield Shield season as his name rose with a bullet as a possible partner for Usman Khawaja at the top of the order.
But Konstas, who was preferred as Marcus Harris's opening partner for Australia A over Bancroft and McSweeney, fell to Mukesh Kumar without scoring in the first over.
Bancroft's poor start to the summer continued when he was out for a duck to Krishna after facing 14 balls.
The Western Australian, who has been in the Test wilderness since the 2019 Ashes, has dominated the Sheffield Shield for the last two seasons but is suffering a form slump at the worst possible time.
Newly re-signed Australia coach Andrew McDonald rejected suggestions the Australia A "bat-off" will completely decide who partners Khawaja in the first Test against India in Perth next month.
"There's a lot of context and consideration around body of work for those senior players in Marcus Harris and Cameron Bancroft," McDonald said on Thursday.
"Clearly Sam Konstas hasn't been able to have that body of work behind him because of the limited Shield cricket that he's played, and Nathan McSweeney is somewhere in the middle of that.
"You take Sam for example, he's had limited experience in Perth, and then obviously up to the Gabba, so there's incredible challenges for players who haven't played in those conditions before, but it's not to say that he can't do that either - he's a fast learner.
"Marcus Harris - of course it's not long ago (in December 2021) that he played a blinding innings out here (at the MCG) against England."
South Australian quick Brendan Doggett was the unexpected star of day one, destroying India A with 6-15 from 11 overs.
Australia A are struggling at 3-28 in the 14th over after tea.
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