Sometimes, when I have magnets in my hands, I think - maybe it is possible to integrate this magnets into wheels or chain and move using their passive energy, without muscles at all?
This question is a variation on perpetual motion - "motion of bodies that continues indefinitely"
According to the wiki article:
A perpetual motion machine of the first kind produces work without the input of energy. It thus violates the first law of thermodynamics: the law of conservation of energy.
In the case of the original post magnets in some arrangement would create movement - work - without muscles, energy.
There is a nice section in the wiki article that talks about the allure of using magnets for perpetual motion machines.
The seemingly mysterious ability of magnets to influence motion at a distance without any apparent energy source has long appealed to inventors.
Bottom line, unless you find a way around the first law of thermodynamics it can't be done.
But it might be worth trying as a learning experience.
No. Permanent magnets can generate force but not energy. For energy, you need batteries, fuel, solar cells, or a hill. In theory you could press two permanent magnets very close together before your ride, storing energy, and release it during the ride to drive the bike. The amount of energy you can store that way is tiny and taking it out as high force, low motion is hard.
Mechanical Doping is a thing. My understanding is you have a small magnet in the rear rim and a device in the downtube that turns on and off a magnetic field as the magnet spins around. For that matter, any electric motor is essentially using a magnetic field to generate torque. This obviously isn't really passive, but it is propelling the bicycle without muscle power. There are still thermodynamic limitations on any system.