When I used my Bootbag it had its own straps. Longitudinal and transverse so stopped movement in any direction. I also used a couple of 25mm cheap ratchet type straps as a "belt and braces" extra. No pun intended.
I now use a solid case with Morgan leather straps. I then use a long ratchet strap ( same as before) to hold the extra high level brake light I strap on, this goes across the case so also stops sideways movement. There is a cheap cover on the caee for extra protection. A large " waterproof" , (well 99%), then holdalls on the shelf inside.
The only downside to using a case is limited rear visibility so wing mirror setting is important. The Cobra light is obscured hence the swoppable extra bfake light. Superseal connectors make this easy.