Hi storming
To answer your question..

Firstly if you pull up the bindweed root, it should look like a long creamy\whitish fairly flexible root, try and get as mich of it out as possible, sadly if you pull it out and a bit breaks of it will come back again.
Secondly, sure you could use round up but if it is wrapped around your plants I would advise not useing roundup especially if you are using a sprayer.
There is a stick of weedkiller you can get called touchweeder, which is waxy applicator and sure it is labourious applying the stuff but it does the job and there is no risk to to your roses and pyracantha.
Hope this helps ya out