I'm guessing it is a sound you hear when you're lifting your finger of the string, so the moment the string looses firm contact with the FB & starts to move a bit (the string still vibrates). Could it be caused by stick-slip? Did you maybe put wax on the FB? Do you see a discolouration from the strings on the FB?
I'd start by a firm polish/rub of both strings & FB, with a dry cloth & focussing at the contact area between the 2. If you did put wax, that needs to be removed, but maybe it's something else that apparently built-up over the years (like from the strings). If that fails, loosen strings, pull them out of the nut & place sideways of the nut (with the bass lying on its back on a bed or so), and then clean/polish the FB with BLO. It the string's outer wrap noticably worn in that area (calliper / µmeter)? Then rotate them 180°. Or maybe a new set, that would qualify as 'worn out'.