Rolands have a dedicated button too. And you can set a pedal to mimic the function of the button. But for all of these boards, you have to press the button once to turn bass inversion "on", and again to turn it "off."
Korg has a cool feature where you can trigger it with velocity. I didn't grow up playing velocity-sensitive keys, I don't have that "touch", and I don't want to break anything. So I'm reluctant to do it that way. And clever though it is, it doesn't obviate the need to play the extra notes. Hence, Roland.
A MIDI solutions footswitch controller and relay connected in series convert bass inversion to the momentary function that it should have had as an option from the factory. Slash chords are a PITA, but they sound good. If there's an easier way to play them, I haven't found it!