You only have three options: pass it around, store it in objects that need it, or make it globally accessible. You can do the latter with a bit of encapsulation though:

my $dbh = DBI->connect($db_info, 'username', 'password',
    { PrintError => 0 }
) or die("Couldn't connect to database\n");

sub get_handle
{
    my $dbh;
}

print "info: " , getdb() , "\n";
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Then you can call main::get_handle() from anywhere, instead of accessing a global variable. It's effectively the same, though it's a little nicer with the encapsulation.