You'd have to create a custom 404 redirect to do that. Joomla needs to know where a user is going and /username doesn't tell Joomla anything. So you'll always have a menu alias in profile URLs. So if you create a public Joomla menu item to CBs profile page then you'll have the following URL.
domain.com/menu-alias/username
The menu-alias tells Joomla they are trying to reach CBs profile page. So for example if your menu item has a menu alias of "profile" you'd have the following.
domain.com/profile/username
Which is exactly what we have here at Joomlapolis. For example my profile URL is as follows.
www.joomlapolis.com/profile/krileon
As for the username in the URL that can be customized using the alias field in CB > Field Management.