CLR is not a natural product. It is a blend of hydrochloric and phosphoric acids together with surfactants. Avoid it like the plague on a bicycle. Hydrochloric acid makes steel rust. Phosphoric is much safer when used as a stand alone product and indeed removes rust. Naval Jelly contains phosphoric.
Now you asked about natural. Vinegar is natural and removes rust albeit slowly. It requires soaking and time. Coca Cola (and Pepsi) contain enough phosphoric acid to attack rust but again it takes a long soak. It also is more expensive than vinegar.
Mechanical means (scrubbing) include Fine (0000) steel wool. I have a friend that used the Mr. Clean Magic Eraser and removed surface rust from chrome wheels.