Depends on the invasive species. I know that Ailanthus tree (aka Tree of Heaven) is very invasive and has made my Yellow Groove retreat from my driveway.

It might be interesting to compile a species versus species battle list of what wins and why.

I think bamboo would do very well...and so would the blackberry bushes. I don't think planting bamboo will hold-off the growth of the blackberries. I've done bamboo digs where the culms were coming up through large infestations of various vines. They seemed to coexist even though the culms were about 20' high and the vines festooned the branches. Just because bamboo can be invasive, doesn't mean it can wipeout other plants, particularly those as tenacious as blackberries.