One method I know about is pulling the vines down off the shrubs and painting them with glyphosate. The vine stems are left intact so that the herbicide translocates into the roots. Flowering time or later is best.

Roundup will work on bindweed but it takes a while to work its way all the way down to the deep roots so you don't want to kill the foliage before it has a chance to do that by using too strong of a solution. If you can untwine some of the bindweed, wet a papertowel with the Roundup, wrap it around the bindweed and then stuff it into a ziplock bag (be sure to wear gloves)and tuck it down into your groundcover while the RU does its work.