As mentioned, you're overwritting the inheritance base creates. Here are three clean solution:

use base qw( CGI::Application Bar );

[download]
or 
use base 'CGI::Application';
use base 'Bar';

[download]
or 

use CGI::Application;
use Bar;

our @ISA = qw( CGI::Application Bar );

[download]

Off topic from the question at hand, are you sure you want to inherit from Bar? Inheritance ("is a") is all too often used when Encapsulation ("uses a") would be appropriate. Without knowing what Bar is, this seems to be one of those times.

In reply to Re: CGI::Application and object inheritance by ikegami
in thread CGI::Application and object inheritance by spork

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