Regarding safety, a bicycle designed for Martian conditions would quite likely use more than two tires for stability.
Why? A regular bicycle with two tires is mostly stable, even in rough terrain, and there are no obvious reasons that is also the case on Mars (I personally use 1 or 2 tires).
However, accidents happen. Most bicycle accidents are minor, and result in a negligible amount of harm. Perhaps you get a bruise, or scratch your clothes a little. No big deal.
But what does a small scratch do to your pressure suit? Potentially a whole lot more damage, with death being a possibility. In essence, small accidents suddenly carry more risk. Some factors also increments the risk as well:
- The cosmonauts would have no prior experience with how forces balance in the environment. Remember that even though the gravitational acceleration is lower, the inertia stays the same. That takes some time to adjust to.
- Even the most flexible of pressure suits is not as flexible as no suit at all. Limited movement and slow reactions are bad for balance.
- Natural terrain. There are no roads or paths to follow. Even if the terrain is carefully inspected before hand, there may still be invisible bumps covered in dust.
Elevated risks are unacceptable so far away from the closest hospital and with an entire mission at stake, so therefore a plausible bicycle design uses a wide, stable base, and multiple tires touching the ground.
Is the soil particularly hard on tires. You could sy that. At the temperatures outside on Mars a standard tire would become rather hard and possibly brittle. And the air pressure in the tires (now X times earth pressure) would need to be adjusted. There might be some more answers on this in question about the wheels for the mars rover. (which are not made from rubber). – Hennes Oct 23 '16 at 14:00