Just telling them is probably the best way .. But it's understandably hard to do.
Remember. Even if you think the answer will be "no" it's better that your parents know .. Relationships go both ways. That includes your parents .. Not only do you deserve to be heard .. They deserve to hear you.
Even if the answer is no, I'm sure they'd want to hear you make the decision to voice your desires ..
That being said, there are "easier" ways out. You can write it out as an email and email them. If face to face is hard. You can approach it indirectly, and start with "If I wanted to go to public school, what would you think?"
Maybe your parents will surprise you.
Personally speaking. I do feel the best way is to "just tell them" .. However .. I also went to public school in brooklyn, and sometimes wish I were homeschooled. I don't know about your neighborhood, but I've found most of the homeschooled kids I met were really awkward .. But later in life as they became adults. They truly set themselves apart, they became more critical thinkers and developed truly original personalities ..
Maybe that's what your parents want for you ..
You could also suggest you want to try it for a year .. To see what you think.
And I'm sure, that'd be lighter on your parents state of mind.
Message me if you like.