Cut it down and as the new shoots grow up spray them with Glyphosate. This is a systemic weedkiller and will translocate into the roots and kill them. If it is well established it may take a number of treatments. Wait until shoots are four to six inches long before spraying.
Glyphosate is available at most garden centres under their generic name - look for Tumbleweed or Roundup if not sure.
It does not have immediate effect - takes 10 days to 3 weeks to show.
http://www.rhs.org.uk/advice/profiles1005/bamb oocontrol.asp