Daas Yochid: I agree that-today- it is accepted that adults do not use bicycles, but it is much more akin to a “gezeira” like “klai zemer”, than an explicit issur.
As far as muktzah, I only commented about umbrellas-which I assume you maintain are muktzah, not about whether muktzah was a “melocho”.
I do realize that ,today, people do not use umbrellas ,or parasols for that matter, due to the question of “ohel. However, there were Poskim that allowed umbrellas in the nineteenth century and I heard-admittedly from hearsay-that in towns in Hungary, there were OPEN umbrellas in the shul, to use if it rained. As they were already open, there was no question of making an “ohel” I will find the sources for you tomorrow IYH.