We get a lot of questions about speeding up Backdrop Designer. Obviously something we need to improve in the next version, but in the meantime...
One trick that I use frequently is to render out at half the resolution (instead of 600x600, render at 300x300) I normally would and then scale the backdrop up to the size I need it. It also helps to apply a 1-2 pixel Guassian Blur after scaling. Since the textures produced by Backdrop Designer tend to be abstract and they're being put in the background anyways, the scaling + bluring don't usually cause a problem. This doesn't always work, especially for textures to be used with 3D modeling, but I'd say about 75% of the time when used for photography backgrounds, it's a workable solution and makes for a faster workflow.
Also, on the menu bar of Backdrop, there's a downward pointing arrow. If you click on that you'll get options for doing a Fast Render. This produces a somewhat lower quality render but is about twice as fast (sometimes more, sometimes less).
Between the two approaches you'll see about a 4x increase.
I've attached a few images, so you can see the difference:
bd-normal : 20 seconds (600x600, normal quality)
bd-fast : 13 seconds (600x600, fast quality)
bd-uprez : 7 seconds (300x300 uprezzed to 600x600, normal quality)
BD-Normal:
BD-Fast:
BD-Uprez:
