Your subs don't include anything that would alter the contents of $bits_10_9. The reason a reference works for the -textvariable piece is that it constantly checks that variable when doing screen-draw updates, but your assignment to $bit_10_9 is only checking those references once (when that statement is executed). You might try making a setbits() sub and using that as your callback. Example:

my $bit_10_9; #yes, this is a horrible abuse of globals
setbits( 0,0 );

my $bit_10_9_mb = $r2Frame->Menubutton(
    -textvariable => \$bit_10_9,
    -menuitems => [['command' => '01',
                    -command => sub{ setbits(0,1); }] ....

then

sub setbits
{
    $bit[10] = shift || 0;
    $bit[9] = shift || 0;
    $bit_10_9 = $bit_10 . $bit_9;
}
[download]

Now normally I try to keep these sorts of globals to a minimum. But without going to OO data structures, it can be difficult to make this sort of data available to callbacks.

updateSheesh, I give the sloppiest answers sometimes. I've fixed this to apply more readily to the situation at hand.