Is there a non-drug, natural way to prevent motion sickness?

Yes and no. Motion sickness is common and can be disabling. It is thought to be due to sensory conflict in the vestibular system. Natural treatment, like habituation can be effective and has few adverse effects, but can be unpleasant and time consuming hyoscine is effective preventive medication for which oral preparations and transdermal patches work. Ginger & bracelets have not been proven in clinical trial.
Ginger. This is not an official medical recommendation because it hasn't been scientifically proven but one common folk remedy is to consume very small quantities of ginger - either extract or the raw root. It settles the stomach. You may still feel dizzy though.