PHP, 18 Bytes
<?=PHP_INT_SIZE*8;
This correctly handles all of the cases of 32, 64 and other bit CPUs provided that PHP_INT_SIZE is correct then, it will show the precise size of the CPU no matter what CPU PHP is running on!
If PHP is running on
32-bit OS PHP_INT_SIZE == 4,
64-bit OS PHP_INT_SIZE == 8,
16-bit OS PHP_INT_SIZE == 2 (theoretically)
8-bit OS PHP_INT_SIZE == 1 (again theoretically)
128-bit OS PHP_INT_SIZE == 16 (Not yet achieved but possible)