I HATE blushing. Ugh! It's a positive feedback loop where you start out embarrassed for one reason, so you blush, then you get embarrassed about blushing.
Sometimes it helps me to actually say, "This is so embarrassing." I don't really know why.
Maybe you could ask to face away from her while you're saying it? Or cover your face? Not sure if you're that kind of embarrassed

. I ask because in my time lying on the couch Freud-style, that was one advantage... not having to look at my T at ALL when talking about the embarrassing stuff.