I missed the '2 or 3' requirement on first reading of the OP. For the sake of maintainability if nothing else, a looping (loopy?) approach may, as you say, be the way to go.

However, there is a simple way to deal with the undefined values produced by zero-quantified captures:

>perl -wMstrict -le
"my $bound = qr{ (?<! [\w-]) }xms;
 my $A = qr{ (?= .* $bound A \s+ (\w+)) }xms;
 my $B = qr{ (?= .* $bound B \s+ (\w+)) }xms;
 my $C = qr{ (?= .* $bound C \s+ (\w+)) }xms;
 my $extract = qr{ \A $A? $B? $C? }xms;
 print '-------------------';
 for my $line (@ARGV) {
   my $s = join '_', my @got = grep defined, $line =~ $extract;
   $s = 'no match' if @got < 2 or @got > 3;
   print qq{'$line': '$s'};
   }
"
"B Bee C Cee A Aye"  "foo C Cee bar A Aye baz B Bee zzz"  "A Aye B Bee
+"
"C Cee foo B Bee"  "xxx C Chuck yyyy A Able zzz"  "A Aye A Aye B Bee"
foo  "A Aye"  "A Aye pseudo-B Bee"  "A Aye XYZB Bee"  "A Aye A Aye A A
+ye"
-------------------
'B Bee C Cee A Aye': 'Aye_Bee_Cee'
'foo C Cee bar A Aye baz B Bee zzz': 'Aye_Bee_Cee'
'A Aye B Bee': 'Aye_Bee'
'C Cee foo B Bee': 'Bee_Cee'
'xxx C Chuck yyyy A Able zzz': 'Able_Chuck'
'A Aye A Aye B Bee': 'Aye_Bee'
'foo': 'no match'
'A Aye': 'no match'
'A Aye pseudo-B Bee': 'no match'
'A Aye XYZB Bee': 'no match'
'A Aye A Aye A Aye': 'no match'
[download]