Don't know about bikes, but I do know about composite sailplanes (gliders)...the owners and the FAA are pretty fussy that refinishing to compromise the structure of these.
The old finish (gel coat) is removed mechanically. The call it grinding, but coarse sandpaper is what is used. The gelcoat is sprayed into the mold as the first step of construction, so the inside surface is rough. The grinding is only through the thin spots. As soon as the glass or carbon starts to show, no more finish is removed. Low spots are filled with bondo or microballoon/epoxy (lighter than bondo, but more effort to sand out flat). The aircraft is then sprayed with gelcoat (epoxy) and sanded out to a smooth finish.
In some cases, the aircraft will just be fine sanded, and painted with Imron paint. This results in a nice looking and durable finish, but adds more weight than the above process.
If the bike was ever polished with a product containing silicone oil, good luck...very difficult to remove enough not to cause finish problems.