You got three excellent answers in a row, covering the three main factors.
A few years ago, a friend took down a multi-trunked holly tree on his property and gave me the trunks. They were too small for any sizeable blanks, but I got some spindles out of it, and had plenty left to experiment with. My feeling was I could use the successful experiments for inlay, trim, marquetry, etc., and learn from the failed experiments. I've also read everything I could put my hands on regarding holly.
So it all depends on how white you want the holly to be vs. how much time and/or $$ you are willing to put into it.
As the three last posters said:
1. If you can wait until the right time,
cut the tree when the sap is down. This helps keep blue and green fungal stains from forming.
It may sound obsessive, but if you really want to have the best shot at getting pure white holly you almost have to be. Soak your chain and bar in alcohol before you make the cuts. The goal is to limit the amount of fungal spores, which are everywhere, that touch the wood. Seal the ends of the log immediately.
2.
If you can find access to a kiln anywhere near you, have the wood kiln dried. Cut the blanks yourself, or have the trunk milled into lumber. A mill near me will mill trees which meet certain basic requirements for $150/hour--well worth it because they could mill a tree the size of yours in about 10 minutes. Then rent, barter, or beg kiln time.
In my experience, even following all other precautions, pure white holly is impossible without kiln drying. Drying schedules are impossible to follow without a modern, computerized kiln. I've tried modified versions of Holly's schedule I could achieve with a convection oven, dehumidifier, humidifier etc. The best I could get is a very nice, acceptable white, with no stain or streaking. But put it next to a kiln-dried piece and the difference is obvious.
3. If you want to try air drying, or if you turn a piece green,
soak the piece in alcohol for at least a day before drying. Don't cover it with wood shavings. Use new brown bags. Do everything you can to keep dust and dirt away from the piece. Treat it like a computer chip factory clean room.
But as was noted by the previous poster, even following every precaution, and even after avoiding any blue or green stain,
it is almost a certainty that air dried holly will develop a grayish cast to it. Again, this might be acceptable.
After all, people who only use the "snow-white" holly are often surprised to see
what interesting grain and figure (especially ray flecks) "lesser" holly can have.
Anyway, there's my two-cent, rambling expansion of what the earlier posters said much more succinctly

Hopefully, it can help you decide what outcome you're willing/able to pursue.
Good luck with the project. And I, for one, would love to hear about your progress and results.
