Clever idea with the earplug, but this bell is not a clapper-type, it's a coil/striker type, seen here:
I tried the electrical tape. One piece worked slightly, but two or more started dampening the bell so it didn't sound nice. So I decided to try my quick enclosure idea.
I found a small box big enough to enclose the bell, and lined it with some scrap anti-fatigue mat foam. I cut a slit & opening for the wires, and temporarily positioned it in place with blue tape.
I closed the machine back up and found this did make a significant difference! I think it could be quieter still, but at least it's not ear-splitting anymore. I'll need to go back in and secure it better too.