Well, I've quit every T I ever saw! So I guess I never became comfortable with any of them. However, my last one was the best. I think it just takes time to become comfortable. Plus, it happens in stages.
There's comfort... & then there's comfort... in other words, there's a degree of comfort you achieve that enables you to talk about some of the stuff that isn't necessarily deeply personal. Then there are succeeding levels of comfort that allow you to talk about more-&-more deeply personal stuff. It's all mostly a matter of time, assuming that the T is someone can bond with to begin with.
One thing my last T always did was to offer me something to drink (coffee, pop, water) at the beginning of each session. It was not only pleasant to have something to drink, but it also gave me something to fiddle with as we talked.