To make sure Wave works with Bitwig Studio, navigate to File → Settings → Controllers. Click Add → Generic → MIDI Keyboard. In the MIDI device drop-down, select Wave's input.
In Softwave solo the function you want to map. Make sure your function has a dedicated CC number or Note (→ see Functions).
To map the function to native transport controls within Bitwig, right-click the parameter you want to map and select "Map to Controller or Key".
To map the function to a 3rd party plugin, first move the parameter you want to map. You should see the name of the parameter displayed on the device in the Fx-chain. Right-click the parameter and select "Map to Controller or Key".
Depending on which of Wave's functions you are mapping, move, tap or click on Wave to make the link.
Now De-Solo the function in Softwave. The function should be mapped to Bitwig Studio.