Your path as a cyclist varies from the walkers considerably. You’re sometimes on the same path, sometimes on a parallel path within sight of each other, and sometimes on roads far from the walkers. Given that cyclists are perhaps 5% of pilgrims, you may be alone at times.
I’ve cycled in many countries, and Spanish drivers were consistently courteous and patient. The roadways were also in good shape with decent shoulders, though the path was occasionally on busier roads than I liked. I had no bad experiences, and I had several nice exchanges with local Spanish cyclists who offered advice and encouragement. Every cycling pilgrim that I spoke with had a similar experience to mine.
Several cities, Pamplona, Burgos, Leon, etc. have long urban stretches, and I strongly recommend having a phone with a mapping application (I used Google maps & the Guthook app) to find your way through. I also took occasional alternate routes when the walker path was crowded and rocky.
I found a Spanish book on cycling the Camino in a Pamplona bookstore that had maps, suggested stages, and which sections of the path that were not rideable. I can’t remember the title after leaving it in SdC, but there can’t be many others. It also helpfully listed bike shops along the way since they were fairly scarce.
The main issue I found is that you’re a community of one since you move at a different pace than the walkers, and you never see the same ones for more than a night. Cyclists are so few and tend to go differing distances, so I mostly rode alone.