Post a photo of the room and you will gather more responses. Also the way it adjoins your bath. And the marble you have selected. And the bedding. Paint comes last so you may wait until flooring is complete. You can paint the bath a different color, but should be a harmonious one. For example, a darker and lighter version of the same shade. Or a blue and a green with similar depth of color. I have BM Woodlawn blue in a bedroom, and it goes from grey blue to grey green depending on the light. If that's too green BM Smoke is a soft blue grey with less green.

You bedroom and bathroom don’t need to match, although they should coordinate. Do you have any pillows, curtains, throws, art, etc that you will be using in the bedroom that have blue in them? I am really bad at colors, so I try to start with an item that I love and pull some colors from it. Since you have bedding, maybe find some pillows with blue?

Pictures of gray cashmere and white dove next to marble, 2 of my grays with marble and white dove, 3 of the grays in bedroom on 2 different walls, different times is day

Pillows on bed

Bedding

a lot of your grays are pulling lavender. Is that what you want? (doesn't work w/your blue beddding)

cooler light is going to make blues look bluer. and anything w/a lavender undertone is going to look purple. As you've discovered. Gray Cashmere has a green undertone.

You'll need to find more of a neutral gray that doesn't swing over into the blue spectrum.

Silver Chain is almost a true, neutral gray. you could try that one.

Or, see if any of these might be better

read this first

https://www.kylieminteriors.ca/cool-gray-paint-colours-the-3-undertones-you-have-to-consider/

You may want to try this one

https://www.kylieminteriors.ca/all-about-sherwin-williams-repose-gray/

a lot depends on the direction your light is from. north and east will lend a cooler light than the other two.

Try Gray Cloud. I used that in my bathroom w/marble and it has a slight blue undertone, no purple. marilyns dress is nice too

Crushed Ice is a nice one.

for better suggestions based on your direction, try reading this

https://www.kylieminteriors.ca/the-9-best-benjamin-moore-paint-colors-grays-including-undertones/

https://www.kylieminteriors.ca/can-i-paint-my-north-facing-room-a-gray/

I never found a blue that worked in my guest bedroom. North and some East light. Everything went Baby blue or gray. BM Soft Fern was a color that did not fluctuate—pretty in all light.

The colors on the bedroom wall are gray cloud, Marilyn’s dress, and bunny gray

And I agree I am seeing lavender undertones!