They only have shrub roses on the David Austen website, for instance.
Now the official answer for this is that there is no particular difference between the two, though some argue that bush roses are smaller, only rising to 2ft. I'd have thought it was the other way round but what do I know.
Me, I just don't get it. I bought a DA shrub rose a couple of years ago - Lady of Shalott I think - and okay, it has grown a bit. But - as with all the other five or so roses in my garden - has a very thin stem, you could use scissors let alone secateurs on the base to cut it. What is the name of those big thick stemmed bush rose structures you see, the kind that frame a front window, or rise up behind a front garden fence? Big, thick, thorny stems the size of your finger. They are not ramblers, they are not climbers, but to lump them in with some piffling shrub rose which while nice enough just isn't going great guns after a few years, what gives?
None of my roses look like growing into the kind of big rose bush I see in other gardens and there doesn't seem to be any way of antcipating how they will grow.