Nope, unfortunately. Only way to do that is to just not turn off BT (this pop-up only shows up when you turn it on). Battery-wise, having BT on all the time (unless actively streaming data/audio) has a very negligible impact on modern phones, so you really won't see a benefit from turning it off other than a handful of minutes of extra juice. If privacy is a concern, then having your device set to not visible should do the trick.