How Do Remove Rust from Bike Wheels and Handlebars?

I've heard that Cola never fails! Do that along with the other advice.

Wad up a ball of cooking foil run it under water and rub on the rust. May take longer than chemicals but is better for you and the environment. Also it won't scratch the surface you're working on.

Oh yeah BTW... Sandpaper will work but takes much longer. Patience is a virtue though, and you will need it regardless.

There are a few things you can use, you need something like steel wool (fine) for is abrasiveness, then some kind of lubricant... WD 40, rust remover, 3 in 1 oil, citric acid or plain water all work well. Make sure you dry it well, then put a nice shine on it with a chrome or metal polish.
Also, you can try to use a wadded piece of aluminum foil in place of the steel wool. works the same or better.

It's cheap and good, parts house, fozz or ospho and you can paint it on or you can put a spray head on it from a quart spray bottle and spray it on let it set till white it will turn white when the rust is dead.) If it hasn't turned white then respray and wait one more day then dry off with rag hit lightly with sand paper and spray paint. The only work on this is how much sanding and picking you want to do to make it perfect.