The hosting Aussies took a 2-0 lead on Monday thanks to a 218-run victory over the tourists.
However, despite being strong favourites to wrap up the series in the Perth Test, which starts on Friday, Bailey has admitted that his team would be "naive" to write off Alastair Cook's side.
"I think it would be a bit naive of us to suddenly think that we had any sort of advantage over them," he told reporters. "We've played really good cricket and we've had even contributions from so many players, and that's been really important."
Bailey had not featured for Australia at Test level until this series got underway.