~As far as I know, bucket names are public via certificate transparency logs.~ There are tools for collecting those names. Besides you'd leak the subdomain to (typically) unencrypted DNS when you do a lookup and maybe via SNI.
Edit: crossout incorrect info
> Besides you'd leak the subdomain to (typically) unencrypted DNS when you do a lookup and maybe via SNI.
"Leak" is maybe a bit over-exaggerated, although if someone MitM'd you they definitely be able to see it. But "leak" makes it seem like it's broadcasted somehow, which obviously it isn't.
I'm pretty sure buckets use star certs and thus the individual bucket names won't be in the transparency logs.