You have the older bystarter. The CL indicates the older type.
It may be a little extra work, but I recommend upgrading to the newer bystarter and a new float bowl. It will make starting a lot easier.
16130-ZW4-F01 for the bystarter and 16023-ZW4-F01 Float Chamber Set. Depending on how the mechanic takes the carburetor off, he may also need 17151-ZV5-000 Intake Manifold Gasket, 17384-ZV5-000 Silencer Plate Gasket and possibly two 16221-ZW4-000 Carburetor Gasket.
Like I said, this will make starting easier.
Otherwise, just order the older bystarter 16023-Zw4-H01.
Mike
By the way, your Serial Number does come up as a BF50D, a fuel injected engine....very odd.