The problem with the code you posted is that the output of a php widget is not a template, so template conditionals won't work. You can use a php 'if' statement like:
Code:
if ($bbuserinfo['userid']")
{
$output = "you are logged in";
}
else
{
$output = "You are not logged in";
}
and the strings can contain html.
Another way would be to use php code to render a template, then you can use template conditionals. I guess it depends on how complex your output will be and whether or not you prefer to use a template for it.