GNOME Terminal in 18.04: Visual bell only?

Apparently, the sound is coming from Ubuntu's alert system. In Ubuntu 18.04, you need to go Setting > Sound > Sound Effects > Alert Volume > Off.

I got this answer from: Turn off error sound on Ubuntu 18.04

A work-around until you find the perfect solution is to replace the bell sound with no sound. On my system the alert sound is found in:

/usr/share/sounds/ubuntu/stereo/bell.ogg

To confirm it is the same sound you hear, use:

paplay /usr/share/sounds/ubuntu/stereo/bell.ogg

Then from this answer: How to disable Alert volume from the command line?, try this:

sudo mv -v /usr/share/sounds/ubuntu/stereo/*.ogg {*.disabled}

Note this disables all sounds. For just bell.ogg use

sudo mv -v /usr/share/sounds/ubuntu/stereo/bell.ogg bell.ogg.disabled