Sure, the constant pragma.

use constant BIT0 => 0;
use constant BIT1 => 1;
use constant BIT2 => 2;
use constant BIT3 => 4;
#...
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That's pretty verbose, though... You could just use a hash, and do

my %bitNames = (
    BIT0 => 0,
    BIT1 => 1,
    BIT2 => 2,
    BIT3 => 4,
    BIT4 => 8,
#...
);
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Of course, you can substitute your more meaningful names for BIT0..BITn...

That handles naming the bits; you could use the vec built-in function to set them, like this:

my $flag=0; # or value from your api
vec($flag, $bitNames{BIT0}, 1)=$newBit;
# you can also use vec to retrieve the old bit values:
print "Value at position BIT3 is:",vec($flag, $bitNames{BIT3},1),"\n";
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--
Mike
EDIT: Added part about vec; I'd only covered naming the bits, and forgotten the other part...