Try not to think about it being about her not trusting you. My T and Pdoc have never expressed it in terms of trust, but rather in terms of serious concern. Since you are a new client, she hasn't gotten a good feel for your symptoms yet, so she will be watchful while she gets to know you.

In my case, in my worst depressions I could become very impulsive. They both witnessed me go from seemingly safe enough in session, to suicide attempts literally just a few hours later, so as they "learned" me, their concern was how quickly my condition could deteriorate.

I would simply have a frank discussion about this in your next session. It can really help to sit and talk about what symptoms signal true danger for you as opposed to thoughts and feelings without that kind of danger. We had many of those kinds of discussions, and they helped me clarify in my mind what steps I need to take at what points so that I can reach for the appropriate help at the appropriate time. Those kinds of honest discussions may be the best way to develop a mutual understanding of the situation.