A variety of manufacturers make snap in wedge bag mounts. The mount attaches to the saddle rails and the bag snaps into the mount. Does know which brands if any interchange?
I have not found a quick connect system that works with different manufacturers, but have found a bag that I can easily swap between bikes without needing to buy two bags.
I use a Topeak Aero Wedge Medium saddle bag and have found on their support website (store.todson.com) that you can buy extra "fixers" to put on each of your bicycles. The medium Aero Wedge saddle bag carries a couple tubes and my compact pump. It has the quick connect and a single velcro strap which goes around the seat post. Very secure.
I have not had any problems with the Wedge saddle bag when mountain biking (I don't go off many jumps but lots of cross country, single track and rough terrain).
After about 4 years, I did have the thin plastic slot thingy (official term I think) on the bag become brittle and crack. I found the replacement on the store.todson.com website and did not need to purchase a new bag, as such I still recommend the Topeak Wedge bags.