I have not had personal experience as I am a pieton peregrino. But, over my many years traveling, I have seen people bring bicycle and motorcycle helmets onboard aircraft. However, the presence of a helmet can be unnerving to some passengers.
Try to buy the brightest color you can find, or at least one that creates contrast with natural surroundings. It adds a layer of visibility and safety, especially on roads.
Remember, the Camino is not a fashion parade. Nor, is it the Tour de France. You can only go as fast as the pilgrims in front of you on a trail, or if on a road, as quickly as road conditions, weather, and your physical conditioning allows. The ride is more of a Morse Code pattern. Lots of walking dots, interspersed with some sprints. Be careful of downhill runs when walking pilgrims might be ahead of you. THEY CANNOT HEAR YOU APPROACHING!
Walking pilgrims are required to walk FACING ONCOMING TRAFFIC. Bicyclists are supposed to ride WITH THE FLOW OF TRAFFIC. However, this has not been my observation over three Caminos. PLEASE PLEASE PLEASE, mount a bell on your bike! The ratchet-supported, "brrring, brrring, brrring..." sound is better for walking pilgrims ahead of you than the spring loading "bing, bing, bing" sound. However, ANY bell is way better for walking pilgrims than no bell. Remember that some pilgrims, misinformed as they are, will persist in wearing ear buds and music players...go figure... I hope this helps...