It very much depends on where you live to what kind of support you have access to. living in or near a big city is always helpful, as not only are the services there to begin with but you have the option to pick and choose to find someone who suits you.
I live on the Sunshine coast in QLD and have found a fantastic doctor and psychologist that works for me, however i had to sift through quite a few till i found the ones that actually listened to me instead of making assumptions and just treating me in the manner that "fixes" the majority.
In QLD [not sure if they're everywhere else] we have the acute care team. If you have the choice and means to, my own recommendation would be to avoid them at all costs. Their front line is arrogant, rude and unsympathetic. they might have changed since i had the misfortune of having to deal with them but when you're at your lowest low they are that last push off the edge. However if this is your only choice, its still doable, just be strong and wade your way through the rubbish till you get to the actual psychiatrists etc behind their front line.
I think from memory a mental health plan needs updating every year, and is a great first step. its unfortunate your relationship with your doctor broke down, as having a GP you trust and have a great rapport with, is so important. I once had a doctor flat out refuse to give me a mental health care plan because I looked "happy and healthy" - didn't seem to matter the plan was court ordered, they thought it was all fake because I could smile. Either way your doctor should have a list, maybe even printable of psychologist and or psychiatrists in your area, and it would list whether or not they bulk bill. Each psych would have their own interests or specialties, so if theres something you deal with along side BPD it could be worth researching or even calling to ask if a certain one specialises or even can recommend someone they know of that does.
The only time I believe centrelink would come into any part of your mental health stuff, is if you were struggling to meet your fortnightly or general criteria they have for you to meet, then you would need to ask to see a social worker there and discuss the issues you're having with them directly so they can let you know your options and any extra services or help they may have available. Alternatively the only other time i can think of is if you were on or were applying for a disability support payment, This would very much depend on how youre affected with your mental health. I know at different times, their minimum of 15 hours work a week, was far beyond achievable for me - whilst i've never been on a disability support payment, I've been in the early stages of applying, but luckily found new support which enabled me to function a little more.
Me--> feels crap --> goes to GP --> GP makes mental health care plan --> doctor gives you plan so you can go source psychologist OR -- Doctor faxes plan to psychiatrist --> psychiatrist rings you directly to make an appointment (or in my case refered me to a different one they thought might be more helpful for me based on my medical history) - from there, you should recieve bulk billed sessions with minimal to no cost. my psychologist costs me $28.90 [vaguely] out of pocket each time.
I've only recently started seeing a psychiatrist and the one i see is totally bulk billed on the condition i bring someone with me - thats just how that particular psych works, having someone with me can allow him to ask them questions about me and their interactions with me.
You just have to weed through the crap till you find a team of people who can help you get to where you need to be.