Parliamentary Speaker Bronwyn Bishop has attacked the Australian Human Rights Commission President Gillian Triggs for being too political in a bizarre showdown on live television.

Speaking on ABC's Q&A show that was broadcast from Parliament House in Canberra, Ms Bishop said Professor Triggs needed to decide if she was to be a statutory officer or a political figure, after Professor Triggs released a damning report into children in detention after the Abbott government got into power.

"Gillian, if I can say, that report of yours was seen by many, including me, as one that was, if it was to be done, should have been done under the previous Government when there were 2000 children [in detention] but you chose to do it afterwards and that made it very political," Ms Bishop said.