Is the school reasonably close to a Metro station and Metro bus line? That seems like the only option if you can't drive your child to school, short of hiring someone to drive your child. I'm figuring here that you child is old enough to negotiate a Metro ride, possibly changing trains, changing to a bus, etc. -- if your child couldn't handle that, public is not an option.
If this is a private school and it has many kids from outside Falls Church, contact the school and ask what it recommends for transportation options. The school might have other families in the same boat as you, and might be more aware of options than we are here on a forum. Maybe there is even a carpool possibility if someone else in Arlington sends kids there. Since the school does not offer bus service, surely it has heard this question before.
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