I can understand why you have a hard time trusting. It took me awhile with my first therapist to really open up. What is it that you are concerned about with your therapist? That you'll be rejected? That she will tell other people about you? Therapists are folks who are known for their caring. You might consider telling your therapist that you just are finding it hard to totally open up right now. Maybe that will sort of break the ice as you see the response.
Some folks are more trustworthy than others. I do think some people can be trusted.