How do I remove the "My account" and "Logout" links? I am trying to sub-theme the Bootstrap theme. How do I  remove the My account and Logout links from the navigation bar?
Try going to Appearance settings on your sub-theme admin/appearance/settings/... and uncheck Secondary menu.

If that doesn't work, check menu settings at admin/structure/menu/settings and make sure you haven't defaulted the main menu to "User menu".