Hey. Realism is alway's highly subjective but when i look at the picture below, there is not much bloomy going on.
But it look's nice
Shaders you could use to rebalance white point or turn light whites into grey:
Personally i am using photoshop+LUT but you could also use:
Lightroom.fx (exposure, white curve) by MartyMcFly
github.com/martymcmodding/qUINT
Or
WhitePointAdjuster.fx by crabshank
reshade.me/forum/shader-presentation/5623-white-point-adjuster
Tonemapping might also help.
It's also interesting to know wich bloom.fx you are using. There are a lot of different bloom effects. Quint also has a bloom effect wich is highly adjustable. You could also have a closer look into
bloomingHDR.fx by BlueSkyDefender wich has an interesting function for auto-adjustment. It's one of my favorites.
github.com/BlueSkyDefender/Depth3D/tree/...native%20Shaders/HDR