Spazboy:

It's very difficult to successfully move a blackberry in the heat of summer, and I would strongly suggest you wait until after a few heavy frosts when the plant goes into dormancy. You are very likely to lose it if you try now.

Seeds would be a last-ditch alternative. Even if you were able to stratify and germinate them, you would be looking at an additional year or two before seedlings would catch up to a rooted plant.

In contrast, it's easy to move blackberries roots when they are dormant, and they will continue nearly uninterrupted growth.

Don Yellman, Great Falls, VA

Don - Thanks for the quick and informative reply. I'll see if I can manage to protect the little bush until later in the year.

Any advice on how much soil to move with the root ball? The plant itself is only about 2'-3' tall and maybe 4'-5' wide.

And should I trim the canes back or not? I am totally unfamiliar with blackberries other than as food.

Some wild species segregate into male and female plants, so you'd want to grow at least 10 of them and then cull out a few of the males. Keep a couple though for pollen.
Again some wild rubus have male and female plants.