for me, the comfort comes from time and seeing how the T responds. there are things I am more comfortable telling "random" people, but there's other stuff that definitely takes trust and being comfortable with the T. With one t, it happened instantly after she responded in a very supportive way to something I was going through. With current T, it's been her consistent patience and willingness to revisit a lot of stupid stuff.
Sometimes comfort is forgone for necessity though. With current T, there was stuff I was really struggling with when I first started seeing her. I had to find the ability to tell her about it, and then hope that it was the right choice... There are still times that I'm not comfortable with T though. I think it has a lot to do with whatever I'm going through at the moment. If too much stuff from the past is triggered, I'm not comfortable with anyone or anything.