I would be prepared to spend a night or two in a hostal. Based on the experience of one trip I think much of this depends on your timing - If you arrive at Hornillos del Camino on a Saturday afternoon (1 day walk out of a major starting point at the weekend) you’ll find most walkers being turned away and getting taxis to other places so no chance as a cyclist. (I stayed in a fantastic hostal nearby with another female cyclist and had the best bubble bath you can possibly imagine)
Popular albergues seem to fill up really early so unless you want to stop riding at midday and queue up you won’t get in. One hospitalero told me that albergues which are the last stop before a big town are usually quieter because most people walk on wanting to spend the night in the town.
I was ‘turned away’ a couple of times on my trip by people who I think were other pilgrims not the hospitaleros. Most memorably, I stopped at Cizur Menor because I wanted to look at the Church and someone started yelling about how I couldn’t stay because I was on a bike and it was far too early – (possibly 4pm?). They relaxed when I said I just wanted to visit the Church. Another lovely pilgrim gave me a lecture about how doing the camino on a bike wasn’t a true pilgrimage and it shouldn’t count, I was also told that because I took the main road in some places I wasn’t doing the proper route and that I shouldn’t be allowed to stay in albergues... but I also met some terrific locals who were amazingly helpful and more than compensated for the odd unpleasant experience.
In my opinion, night (or early evening) on the camino is wonderful, no pilgrims to worry about terrifying with your bell and lots of locals out taking a stroll. Nothing to worry about, it’s not creepy, I would say take advantage of the freedom a bicycle gives you and really embrace the experience of cycling the camino.
Good luck with your ride!