A bicycle allows us to use our strength to go faster, rather than having to move our muscles faster, we can just push harder. It also more directly converts the energy we are consuming into forward momentum than our walking style does. We are pretty efficient at processing the energy out of what we eat and into work done by our muscles, but beyond that, there are certainly locomotion styles that haven't naturally evolved yet that would singnificantly improve how fast we could travel using that energy. Until then, we got smart instead, which really helped.

There are technically types of wheels in nature, but not in animals, the way alot of bacterial flagella operate is basically a wheel. Or more accurately a biological chemical/electric motor, but it spins anyway. And some of them can rotate either direction by engaging a protein cluster that effectively acts as a "reverse gear" like a transmission.