Hi BipolarKitten, welcome to the forums.
I see my Psychiatrist through Telehealth, however I'm in regional Victoria and don't have any Psychologists around that bulk bill, take new patients and will accept me aswell as other mental health facilities (had a traumatic experience at the Headspace centre but maybe it might be helpful to you if you're 12-25). I'm not sure if they'd do it for capital cities, I think it's only places that are regional with no access to professionals around.
However my advice would be doing a Google search to see if you're eligible, otherwise seeing if there's any you can see face to face because that may be better.
Best of luck, take care.