Hi, 

If you are weary about using chemicals you can just cut/dig/pull and keep doing so if the bindweed or any part of the roses come back. Eventually they will use up the root storage and will stop growing back.

You can also carefully spray or paint the foliage but understandably you would want to be cautious. As long as you wear gloves, long sleeves, pants etc. and don't apply on a windy day you should be safe. 

You won't need to treat the soil for the rose rosette if that is what you were referring to. Rose rosette disease travels by a mite through the wind and won't stay in the soil. Also, it won't get on the summer sweet. 

Let us know if you have further questions.

Emily