I need a bathroom paint that definitely will prevent staining

I don't know if any paint will not stain with hair dye. A glossy paint would repel the most, but it still may stain some. Hair dye is nasty for coloring everything. I know, I have a lot of old towels my daughter used to color her hair, but never managed to get any on the walls. Perhaps glossy tile with no grout would not stain.

My recommendation would be to get your hair colored professionally. If you can't afford that, check out a local beauty school, they are very cheap and the instructor supervises.

Why are you shaking your head so violently that you get hair dye on the wall? Get your oldest towel or buy a black one. When you apply the dye to your dry hair, wear gloves and follow the directions. Then wrap your head with the towel, like a turban. When it is time to rinse, do so in the shower or tub, not in the sink. Hold your head completely under the running water and gently massage your head. Don’t open your eyes! Keep rinsing and massaging until you can feel only clean, not sticky hair. Finish your bath or shower and use a dry towel on your hair. Do not shake your hair dry. Use the clean towel and a blow dryer to blot and shape your hair. Wash the dye-ing towel by itself or with other older black clothes. If the towel dries before washing, the dye will stay set. I hope this protects your walls and your counters. Best wishes 😇

What a pain. My bathroom is painted with Dutch Boy semi gloss and I have not ever had this wall issue. If I do get some on the wall during application, it always wipes right off with a piece of wet tp. Because the walls are stained with dye now, I would definitely use a primer and because it's a bathroom a primer with mold resistance.

I do my roots in the bathroom and sometimes there will be a bit that somehow lands up on the counter or even the floor on occasion (easily wiped away) but I have never had it spatter on the walls. I don’t think that your problem is with paint but perhaps how you are applying the colour. Are you using a colour brush and sectioning your hair or just slapping it on? If so that could be why it’s splattering. If it is a box colour it probably doesn’t have a very thick consistency, hence the splatters. At any rate we have found some success using hair bleach or 20-40 volume peroxide to remove dye stains. Btw I own 6 hair salons and have been in the business for over 30 years. I would have one of my stylists doing my touch ups but the closest store is about 300 miles from me. Just in case you wondered why I’m doing my own hair in the bathroom :-)

Thank you Nancy for your suggestion ,I'll have to give that some thought.

The paint that I purchased was gloss but as you said ,it still stained.

Thanks ,have a Happy Thanksgiving