Hi @JensS
Welcome to the Sonos Community!
Is the Move flashing green when you try to add it? If not, the process will fail.
Please follow the steps on our Reset your Sonos product help page to reset the Move. Once done, it will flash green and be ready to set up. In the Sonos app, select Settings » System » Add a Product (but only do so if the app connects to your existing system) to add it to your system.
If this fails, I recommend powering off your router for at least 30 seconds and trying again once WiFi returns.
As @Airgetlam mentioned, the Move will need to use your router’s WiFi, not the one created by the Bridge, but the app will sort all that out during setup.
Edit: Added link
"Common sense is the collection of prejudices acquired by age eighteen." - Albert Einstein