OK - you could try this. Drill a 10mm hole around 6 inches deep and pour in some granular sodium chlorate weedkiller through a funnel. Ignite with a blowtorch while wearing safety goggles - (it spits a little).
After the combustion has completed, inspect and decide if drilling several holes and filling with weedkiller will benefit.
The only danger with this is getting any on the aforementioned bush - it's quite a good weedkiller, though one or two crystals won't kill a large bush.
Mr F.