Where can I find a list of cities with public bicycles available in Europe?

This is maybe not exactly what you're looking for, but fluctuo^{not affiliated} is a shared¹ mobility aggregator that provides a map where it lists all available shared¹ vehicles (bikes, scooters, mopeds) on a location.

Additionally, there is a Github repository that lists bike sharing systems that publish their information in accordance with the General Bikeshare Feed Specification (GBFS), which is a standardized data feed for shared mobility system availability.

^{1: It's actually all rental mobility, as one always has to pay for the service of using a vehicle. It's just that the vehicle is not rented out at a single location but on different locations in an area.
Clever marketing has spread the term "shared mobility" to give it a friendly and less profit oriented vibe.}