Privacy on XBox Live
Solution 1:
The easiest way is to bring up the mini dash (with the guide). Setttings page-> Preferences->Online Status->Appear Offline. This is also where you change it back to Online, Away, or Busy. Youtube Guide
If I'm 'sick' from class I usually unplug my ethernet cable first, sign in with my profile, change my status to offline, and then connect to live. I'm pretty sure this stops it from showing up as signed in X hours ago.
Solution 2:
There is an option to set yourself invisible.
Guide > Settings > Preferences > Online Status > Appear Offline
You cannot set yourself offline to just one person, it would have to be to your whole friends list. Once you do want to appear online set it to Online.
Also note, if your Gamer Tag auto signs on when you start your X-Box you might want to unhook your Ethernet cable. Once you set your status to offline then you can plug it back in and play online without being detected by your boss.