... my problem has to do with calling internal methods since they dont get the $self as their first argument ...

If you use a normal (non-OO) subroutine invocation, then you're invoking a subroutine, not a method. It's fine for a package to include subroutines as well as methods, though it makes the code harder to subclass and extend.

Since you seem to want access to $self from within the private method, you probably want to do something like

  sub _bar {
      my $self = shift;
      ...
  }
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and invoke it from your public method via

      $self->_bar("do something");
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Note that I've written _bar instead of bar. That's a convention that some use to designate that a method is private.