while (<DATA>) {
   my $c = () = /\Q$bit\E/g;
   $hash{$_} = $c if $c;
}

my @rank = sort{ $hash{$b} <=> $hash{$a} } keys %hash;

my $to_print = 10;
$to_print = @rank if @rank < 10;
print "$_: $hash{$_}\n" for @rank[0..$to_print-1];
[download]

Avoided intermediary array. Converted $bit from plain text to a regexp using \Q..\E. Produced better output.

If there are two (or more) identical lines, they will only appear once in the hash, but that doesn't look like a problem.

Update: I just noticed there's a question at the bottom. But I don't understand what you're asking anyway.