It takes a looooooooong time, but when I last stripped paint of a bike for incredibly cheap, I used strips of sandpaper, wire brush and emery cloth to strip every last bit off. This is probably the slowest possible method, but it is really cheap and is unlikely to damage the metal.
However, considering the year of your bike, I would assume it is aluminum. As such a chemical stripper would be even less likely to compromise the metal. I have never personally used it, but Jasco Aircraft Paint Stripper has been cited by many here to be the most effective.