This is an updated model of of the Altura bag I use...last one I bought cost me £25.
Altura | Aero Rack Pack
It comes with a seperate piece I think they call it a "landing stage" or something similar.
I fix this to the rack with some ten or so small plastic ties, the bag then is velcroed to this, the bag can then be fixed or removed at will.
...however I prefer a more permanent fix and I cut a piece of hard plastic to size , this fits in the base of the bag and I then use 2 heavy duty plastic ties to make a permanent fix to the bike.
....reasonably safe and very secure ...and "bags" of room in the bag.