Unless you are isolated from it (i.e. surrounded on all sides by bindweed
free gardens or areas) you will never get rid of it and need to live with
it. This is my situation ("wild" hedges around garden and non-gardening
neighbours) and I've found the following reasonably successful as a way to
manage it:
first - treat all possible with glycophosphate.
second - dig up all you can.
then pull off all the growth (of the untreated weed).
finally try to walk around the whole garden at least once a week pulling up
(or spraying if possible) any new growth.
Much of mine is now at the weak and spindly stage and I've only been doing
this for a year. It does take persistence though.

--
Hayley
(gardening on well drained, alkaline clay in Somerset)