I think it's very natural to be afraid to open up about these thoughts to a therapist. I also find it difficult to approach some topics, so I often make a plan on how to approach them to make it feel more natural. If you feel guilty for having these thoughts, please know that when we see no way out, they can force themselves upon us, and the therapist should know that as well. I think a stepwise approach to ease into this topic could be like this:
You could approach the topic slowly, by talking about the feelings which cause you to want to CTB. Did you talk about those feelings before? If so, you could say that they came back or are stronger now. You could say that you are afraid that these feelings might not go away or get even worse. Then go closer to the topic by saying that sometimes you'd wish you would not wake up again. The therapist should notice that you're hitting sensitive ground. You could go on by sharing that you have fantasies of dying by some method. Then he should ask whether you'd actually do that, and then you're almost there.
I hope this is not too detailed, but it's the way I make plans to share sensitive things for myself to feel safe.
Another way would be to request a depression assessment test because you fear things have gotten worse. These tests usually include a question about suicidal thoughts, and you could check the corresponding box there, hoping that he'll take that as a reason to inquire further.
I hope you will find a way to share it that you are comfortable with, and that your therapist will react with empathy and care, but without judgement!
