Billing 96101

I am reaching out to the community to see if anyone has experience with billing 96101 codes as a Clinical Trainee or predoctoral intern? I have my Master's degree in Applied Psychology, which qualifies me to do psychological testing. I also have nearly completed my 2,000 hours internship requirement toward my PhD in Clinical Psychology (all necessary coursework is completed). I still will be working on my dissertation however. At the conclusion of my internship, will I still be able to bill 96101 under the supervision of a licensed psychologist for private insurance? If an organization has any input, it would be greatly appreciated.