Didn’t we just have this conversation last week about a different one of your fixtures?
All of the same discussion applies. A buzz is the result of a vibration and varies depending on the combination of switch, fixture, bulb, and wiring. Sometimes it just takes trial and error.
We would need the brand and model number of the mirror, but it’s very likely that it has a transformer built into it. So all of the same issues apply.
Also, we just had a conversation about dimmers with non-dimmable bulbs in a different thread with somebody else last week, so I don’t want to go over all of that again. But the short answer is in general you should not use a dimmer with a non-dimmable bulb unless the switch itself has a parameter which lets it be changed to act like an on/off switch. 100% bright is not the same as on, the physics are very different.
In your case, it’s even worse since your mirror has its own internal dimmer control. The two dimmers are very likely to confuse each other and burn out one or the other or both.