I think the fact that you say you really like your therapist and think she'd be supportive and try her best to accommodate if you addressed this sounds really good. When there's something I find really difficult to talk about I tell my t there's something I really really want to talk about because it's been bothering me for a while but that it's really difficult for me to tell her because of shame/fear of rejection or conflict or whatever it is that time. She then gently guides me through it and it's always been such a lovely experience of being able to talk and something I've felt has been really shameful or like a dark secret and then once it's out in the opening with her she gives me so much lovely reassurance that it all of a sudden isn't a shameful horrible secret anymore.
Why don't you try something like this.. I'd really like to talk about something that's bothering me but I'm scared of bringing it up because I don't want you to feel criticised/upset/I don't want to come across as confrontational... And they say the eating issue is a really sensitive and complicated topic that you feel you need help and support with.. but that recieving any practical tips about healthy eating etc really triggers shame or whatever exactly the feeling is for you and it feels really unhelpful for you. And that you wonder if there could be another way for you to work around it together that would be more helpful. If it's too difficult to say you could write it and email or give the paper to her. I often do that if it feels too tricky to say.
I've had an eating disorder for twenty years now. It's been more on the background while I've been pregnant/breastfeeding (last almost ten years) but now that my body is mine again it is a properly full-blown bulimia/restricting/binge-eating with the horrible weighing and checking in the mirrors multiples times a day. It's taken over my life again. My t has been really helpful though. Her main focus has been to understand the pattern behind this.. I thinks I'm not enough or am too much for people and overcome by guilt. I don't think I deserve nice things so I deprive myself of food until I can't take it anymore - binge-eating need to get rid of it.. etc. She tries to work with my self-esteem and how I view myself and talk to myself as a priority. She never comments on it when I binge. Apart from saying all bodies need food and it's sometimes normal to comfort eat and that if I do binge I shouldn't beat myself up about it. It's only the restricting that gets her really animated and bossy. But in a nice way. She gets really annoyed and lectures how I won't be able to survive with food and how I'm setting myself an impossible task and need to be kinder to myself.
I've found my ts approved to eating problems really helpfulness and definitely feel like my thoughts are slowly beginning to shift. PM me if you want to talk about this anymore. Google overcoming disordered eating module. That's an amazing resource for any trouble with eating. Im using it and loving it!!
Hope you manage to get it sorted.