Arky, I've had my lottie for a year and the trick with bindweed is:
Wait until it's growing, then nuke it with weedkiller spray that gets into the roots. It's the only way (for me).
I also found a good way to target the bindweed precisely is to put loads of stakes around the area. Bindweed likes to climb up them and when it's covered in leaves spray them then.
That way you don't contaminate the soil or plants around them.
I would like to add that this handy hint was given by a forum member, but I can't remember which one, so proper acknowledgement can't be given!