I think during the summer it takes about three to size weeks. It also depends on if the weather is hot, dry, cold or wet. It might take longer or shorter.
What I did that worked really well was boiling my deer head for about two hours. Like I said it works well but stinks up the place like heck. The smell of boiled brains is nasty:(
Hope you find a good way!!!
Find a hot-plate (good luck) and boil it outside. That's what I did with mine. Plus, Make sure if you use bleach or any other liquid to whiten the skull, do NOT get it on the antlers (also, good luck with that!)