It is important to remove any grease before bleaching.This isn't always needed with deer but sometimes it is.When you are sure the skull is dry,if there are wet or waxy looking areas,that is grease.If it all looks dry,you are good to go.
The bleach you are talking about will work fine.I apply the bleach paste and then wrap the skull with cling wrap overnight.This keeps it wet and that keeps it active.Unwrap and rinse the next day.
After bleaching and drying,it should be sealed.The best thing I have found is Future floor finish,thinned 50/50 with water.This will soak in to all that porous,dry bone and not only seal but helps with the brittleness.Saturate the daylights out of it.
After the sealing and it drys,hit any loose nasal bone seams and teeth wit a little Elmers glue to tighten them up.Future is water based and will soften Elmers,so Elmers AFTER sealing with Future.
Cutting the Future with water:
1.Helps it penetrate deeper.
2.Makes it go farther-cheaper.
3.Keeps it from being shiny.
When finished,it won't have that dry,chalky feel but will feel more like a smooth eggshell.
If you get any bleach on the antler,it will take some color off but holler and I'll lay out how to get that back very easily.