How to prevent algae formation in basin pipe?
Two things spring to mind. Algae are green plants, so lack of sunlight is an effective deterrent. Switching that translucent white pipe out for an opaque black one or going crazy with the duct tape should help. (Ideally a smoother pipe, Ed Beal style.)

Second, potassium permanganate (KMNo4) is very effective against algae. I don't see how you'd get it to stand in the pipe long enough to do anything though. It's typically sold in either pool/spa supply houses or aquarium dealers, usually under some sort of brand name. I can't imagine it being easier to find than bleach, but it's worth a look.