The reference to 'Bardou Job' being triploid seems to come from the 2016 publication, but in that they record their source material as coming from the Loubert Rose Gardens, and that presumably coming from Loubert. The Loubert website shows a double rose which seems to correspond to the "Bardou Job - in commerce as" in Europe, or the "Alcatraz Red Climber" in the US (are they the same? I can't tell), but in any case it doesn't appear to be the authentic variety.
I'd suggest the real 'Bardou Job', as found in Australia, is probably tetraploid.