package Bug;
sub print_me
{
    my ($self) = shift;
    # The @_ array now stores the arguments passed to &Bug::print_me
    # The rest of &print_me uses the data referred to by $self 
    # and the explicit arguments (still in @_)
}
or, better still: 
package Bug;
sub print_me
{
    my ($self, @args) = @_;
    # The @args array now stores the arguments passed to &Bug::print_me
    # The rest of &print_me uses the data referred to by $self
    # and the explicit arguments (now in @args)
}