I am unaware of any Maria Montessori writings that discuss how to teach a child to ride a bike, but that doesn’t mean she can’t be the inspiration for our approach to this rite of passage.
The Montessori idea that the environment (equipment) should be built with the child in mind inspired our family to look past the typical children’s bike with training wheels. I recall “learning” to ride a bike with training wheels and then having to (really) learn to ride a bike without them. It was not a smooth transition for me, they were totally different skills and having training wheels did not give me confidence but rather left me dependent and scared for their removal.
Thankfully other inventive folks understood this same issue and set out to try a different approach. It was deduced that balance is the hard part of bike riding not the pedaling or steering, as any observant parent who has ever seen a two year tear down a drive-way on a tricycle could tell you. So instead of buying the large bike with training wheels, how do you begin?
Begin with the balance bike! Our balance bike, that was purchased on a whim from a discount site, has been the key to our bike riding success! My daughter used the balance bike for about six months and my son used it for over a year beginning at 2 years of age. My son at 3 was so successful with the balance bike that he could run and glide at a similar speed as my daughter on her “real” bike.

This is a similar version to the balance bike we used. You can get it on amazon.
After success with the balance bike we moved to a 12-inch bike which is the same size as the balance bike just with added pedals and brakes. It took my daughter about 4 hours over 3 days to master the new bike. My son took only about 30 minutes! He is still learning to brake and stop without rolling into the grass, but the progression has been extraordinary. My now 6 year old gifted her 12-inch bike to her brother and earned a 16-inch bike for her birthday. This incremental increase in size could become cost prohibitive so we expect to purchase all future bikes at garage sales or Craig’s List. My children are not biking geniuses, we just set them up with appropriate equipment and the ability to feel successful.