I would expect both: the “Show interface” button and the outline disclosures to be hidden when coming back to Bike (as they were when I backgrounded Bike).
Not sure if you’ll like this better, but at least it’s a bit more consistent. I’m syncing the control (plus that button) visible state to NSCursor visible state. So any action that hides mouse caret will also hide those controls. And any action that shows mouse caret will show those controls.
Generally this means if Bike controls are hidden, and then you use keyboard to (Command-Tab) to go back to Bike, controls should stay hidden. On the other hand if you use mouse controls will show.
Anyway, give next release a try and see what you think.