Welcome to the "Order of the Bowl", Markelberry.
All three instruments you have acquired are worthy and capable of lovely music-making. Onwards, then...
There is nothing particular, I suppose, to playing a bowlback "the right way": good, clean fingering, coordination, etc. will serve you as well as on any other type of mandolin. Perhaps the very first step is to try to establish good posture; all method books I know of have some pictorial advice as to how to hold a bowlback comfortably and securely.
Beyond that, there is the issue of related, bowlback-specific equipment: light very, VERY light! strings, and a pointier pick than what you would use on carved instruments. You may also have to adjust your grip to accommodate the olive-shaped pick; again, method books are most illuminating in this respect.
I am sure you are aware of all the extant methods, as you are, of course, an experienced mandolinist. Any one of them would do; it will, however, take you a little while to get used to the comparatively shorter scale of the bowlback. Having said that, and as direct benefit of said shorter scale, you have immediate and automatic access to the vast, enormous, monumental literature of pedagogical works for the violin, most of which should carry over just fine on the bowlback.
Enjoy your bowled critters in good health and cheer!
It is not man who lives, but his work. (Ioannis Kapodistrias)