You're nearly there. Two things that you need to improve: you don't need escape the star in the character class, it's just [^*]; and ($bagofwords)+ will only capture the last match of that regex.

Here's something that nearly works:

use warnings;
use strict;
use 5.010;

my $line = '*Mary* had a little lamb';
my $bagofwords = qr{had |a |Sam |Tom};

if ($line =~ s/\*([^*]+)\*\s*((?:$bagofwords)*)/*$1 $2* /) {
    say $line;
}
[download]

It outputs *Mary had a * little lamb. If you want to include the underscores, you might have to post-process $2 before interpolating it, possibly with the /e modifier.

In Perl 6 a quantified regex just returns a list of match objects, so that's a bit easier here:

use v6;

token word { had | a | Sam | Tom  }

say '*Mary* had a little lamb'.subst:
        rx{ '*' (<-[*]>+) '*' \s+ [<word> \s+]+ },
        { '*' ~ join('_', $0, @($<word>)) ~ '* ' };
[download]

Output: *Mary_had_a* little lamb

(Note that Rakudo doesn't yet implement s///, but the method form of substitutions work today)