Is there any provision about commuting in your contract that allows him to have a say in this matter?
Because there isn't in the law. And his actions have to be based on something. The USA is a country following the rule of law, meaning he can't just make things up. He needs to have some kind of legal foundation for his request, otherwise it is just that: A random stranger asking for something, and you are absolutely free to honour his request or refuse it or even ignore it without saying a word. Without a clause in your contract, he is in the same legal situation as the guy at the subway entrance asking for pocket change.
It is very, very unlikely that there is a clause in your contract regulating how you are allowed to commute or who has a say about it, but we can't be entirely sure because you can sign any contract you want, so go check.
If there isn't, then see above. The question now becomes: How do I politely tell my boss that this isn't any of his business and his power ends at the work time and company grounds borders?
A friendly but strong answer would be something along the lines of:
"Boss, I cannot find the clause in my contract that regulates commute
methods. Since my commute is not paid company time, but unpaid private
time, I believe I am free to choose whatever method suits my personal
needs most. Please let me know which contractual obligation I seem to
While this shows clearly that you know your rights, and IMHO you need to show bullies that you are standing on stronger ground than I am to avoid a confrontation, it might seem too strong for you. But given what you write about your manager, I don't think he'll take anything less than that. On the contrary, I think you should be ready to take this up one level to his boss or to HR, depending on his answer.
(also, the health benefits of biking outweigh the dangers, which are probably smaller than driving though that depends on where you ride so I wouldn't try an argument from facts unless you have all the facts, specifically for your region and route)