I have a list for new therapists about what kind of things are good for me to hear and which are triggering, after having different experiences. They have all appreciated this input as it helps the do their job better. On the list I include things like I need them to treat me like a person first and deal with my issues second, I need them yo listen to my input on what I need and what will/won't work, to basically treat me like am expert on myself as much as they can. I also told one t that in order for me to be ok opening up about my different parts and emotional issues I need to feel like she likes me as a person(in a professional manner) because I'm very sensitive to judgment, whether it's real or perceived.
I would also suggest talking to your t about talking and opening things up. I feel more comfortable if we both know what to expect and where the insecurities lie in opening up. It opens the door a bit without having to become very vulnerable. I've also asked different ts how they respond with other clients who have similar issues. It was a good way fore to feel a little more comfortable switching in front of my t once I knew that we were on the same page as far as her talking to them. For instance, she does a lot of CBT with me, challenging my wording or perception on different things, but that approach would be harmful for my younger parts to deal with. So before they ever came out in session she already knew that it's better to just talk to them and validate their feelings, instead of challenging their thoughts. The same could go for if you were going to bring up a triggering topic. How would you like your t to respond? What do you need to hear, or do to feel comfortable, etc.? Do you need to have a grounding exercise ready, do you need extra time or validation, does it help to hold a stress ball or play with playdough to keep your mind in the present?
Exploring the topic together beforehand can help build trust between you and make the experience less scary as well.
IJ