BobCo,
I posed the same question on another forum and someone said that they just tie their soft bow case on. I did some work with mine this afternoon and so far, it looks like it will work well.
It' s pretty small and held on secure with the straps behind the cantle, that I' ve run through the handles on the case. The front is tied on with the front straps as well as my rope holder. I' ve folded over the excess of the case with some twine because my bow is much shorter than the case, and that makes it very compact. The only concern I have, is being able to get out of the saddle quick if the need arises. Because the case hangs off the saddle, and over your leg, there is a potential for getting hung-up, but I don' t consider it a significant hazard by any means. You leg will also keep the case away from the side of the horse.
Now, saying all this, I' ve not had it strapped on to my gelding yet. I will be doing that in two weeks time and will let you know how it turns out.