I would use Class::DBI to build a module MyApp::Db whose sole job is handling all database work (your add/delete/update logic).

package MyApp::Db;
use base Class::DBI;

__PACKAGE__->connection('dbi:mysql:dbname', 'username', 'password');

1;

package  MyApp::Db::User;
use base MyApp::Db;

__PACKAGE__->table('user');
__PACKAGE__->columns(All => qw/id username password/);

...
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Then your RunModes:: only need to use MyApp::Db objects to do database operations, and there is no need to pass a $dbh around.

package RunModes::User;
use MyApp::Db::User;

...

sub validate_user {
  my $self = shift;
  my $q = $self->query;
  my $user = MyApp::Db::User->search(
               username => $q->param('username '),
               password => $q->param('password')
             );
  if($user) {
    # laugh
  }
  else {
    # cry
  }
}
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