he is most likely in the Pokemon center unless you have not yet beaten the gym
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Get the 7th badge from cinnibar island then you will see Bill outside of the gym say YES to his question to be transported to one island!
The 3rd gyms badge will grant you the ability to use Fly outside of battle, the 3rd gym is in vermilion city.
The celadon city badge AKA the Rainbowbadge courtesy of beating Erika at the celadon city gym.
beat everyone in silph.co and you can get into the saffron gym
The fourth gym at Pokemon fire red is grass type gym