I'm 22 and my folks, while supportive, are still very nervous about me commuting via bicycle. This is compounded by the fact that I cross over a major freeway and have to ride in some 40mph traffic (which inevitably means the motorists are doing 50+, seriously). I understand how nervous they are, but fortunately they are accepting and... I don't live with them so while they were skeptical I just did it.

I wouldn't advocate sneaking these things, and I wouldn't advocate "breaking the rules" (count yourself lucky that you have parents who do care about you - mine do but so many of my friends literally despise their parents to the core and it kind of makes me sad that they do). Rather I would advocate sitting down and seriously discussing it with them, bringing evidence of its benefits (health, money, etc) as well as proof that you've researched the safety concerns and understand the risks. Go from there.