Can an inpatient of a private psychiatric hospital attend bulk billed outpatient appointments whether by telehealth or face-to-face?

This question came from a consumer.

I am an inpatient in a private mental health unit in a private hospital. I am under an inpatient psychiatrist. While I am an inpatient, I have a telehealth review consultation booked with an outpatient psychiatrist who is known to me. I also have a review consultation with an outpatient specialist in person, and a review consultation in an outpatient clinic at a public hospital. I am allowed to leave the private hospital to attend the in-person consults and will then return. But I have heard that these services can't be bulk billed. I am a pensioner so cannot afford private fees.