our $bob;
local $bob;
$bob = 'bob';

##</code><code>##

use strict;
use warnings;

package MyModule;

sub do_it {
   my ($arg) = @_;
   our $VERBOSE;

   ...

   warn(...)
      if $VERBOSE;

   ...
}

sub do_it_quietly {
   my ($arg) = @_;
   our $VERBOSE;    # Avoid saying $MyModule::VERBOSE
   local $VERBOSE;  # Save existing value.
   $VERBOSE = 0;    # Disable logging.

   do_it($arg);
}

1;