I dug up some rose bushes in my old house - just to move them to the border so I could turn the central beds into lawn. Most of them had been there at least 20 years, but they nearly all survived! (One or two were just too big to move).
The main thing is to disturb the roots as little as possible - try to keep the main ball intact with some earth round it. Wrap the root ball in sacking (burlap) and keep it moist. You can also wrap the stems in this to make it les prickly to move! You should trim off any really bendy stems as they will get damaged anyway, but don't cut too far down at this stage of the year. when you get to the new house soak the roots overnight in a bucket if you can. Otherwise dig in plenty of well-rotted manure (or similar), plant the bushes and water well in. A little feed will help them overcome the trauma!
For other bushes, depending on how well established they are you might be able to divide them and just take part with you, or else get some cuttings rooted now. I'm not sure how it works there, but over here you cannot empty the garden of established plants unless you have agreed that with the buyer first.
I must add I am no expert - this is just my experience of moving stuff around!
