You have your boss's phone number, right? As a matter of decorum you should at least do it over the phone. If they're hard to get hold of, then email something

You have your boss's phone number, right? As a matter of decorum you should at least do it over the phone. If they're hard to get hold of, then email something like, "Is there a good time to call you today?" or (only slightly deceptive) "Could I call you to talk about the next things I'll be working on?"