I have no idea what hold ups are, but the thing that is important to how you wash a thing is what the material is. In general, oxygenating whiteners like OxyClean are a safer way to whiten things than chlorine bleach, so unless the material is something that this is known to be a bad idea for, I would try a soak in that.

Not a lady and have no hold ups, but if you want your whites to maintain that crispy, clean brightness, you should try Mrs. Stewart's Liquid Bluing. That shit's magic.

Hold ups?

Is that a Bra?

I just toss mine in the wash but I also do not give a damn so like... 🤷🙃 Also, to be fair, have never been a fan of them myself and can't say I've worn them more than like a handful of times in my life.

You can try a bleach dilution on an older pair. Something you might otherwise throw away. Start with 5:1 water to bleach and try stronger concentrations until you get the desired results. Make sure you measure and record your measurements so you know the ratio that works best

Disclaimer: This could ruin your clothes. You should see what others have to say before trying. I'm a scientist not a... person who knows useful things