/(?:(?!$re).)*/
is the equivalent of
/[^$chars]*/
but it can (negatively) match entire regexps instead of a choice of characters. Keep in mind that both expressions can sucessfully match 0 characters if not properly anchored.

s/(.*ing)(?:(?!bob|fred|bill).)*(more)/\1HIT\2/;
[download]

Update:

You may want
"something that isn't /bob|fred|bill/"
rather than
"something that doesn't contain /bob|fred|bill/".

The code for that would be:

s/
   (.*ing)
   (?:
      .{0,2}
      |
      (?!bob).{3}
      |
      (?!fred|bill).{4}
      |
      .{5,}
   )
   (more)
/\1HIT\2/x;
[download]

or

my %bad_words = map { $_ => 1 } qw( bob fred bill );

s/
   (.*ing)
   (.*)
   (?(?{ $bad_words{$2} })\A(?!\A))
   (more)
/\1HIT\3/x;
[download]

You could simplify the above to

s/(.*ing)(?!bob|fred|bill).*(more)/\1HIT\2/;
[download]

but only if the start of more can't match the end of bob, fred or bill.