sujiwan- I have some of that grass from hell, it's very hard to deal with. A black plastic barrier or weed fabric might suppress it over time, or it might find chinks to grow through. I think killing it out would be your best bet.

A gc I have that is tougher than grass is ground cover Comfrey, Symphytum grandiflorum. I haven't tried it under roses, just under fruit trees. It gets around 6-12" tall. Vinca major once established is tougher than most grasses, though some can seed into it. It gets rather tall, though. Most of my other good gc lets grass grow up through it, so it's really hard to get rid of the grass- Vinca minor, Rubus calycinoides, Arctostaphylos uva-ursi, etc. Mulching really deeply to partially smother the grass and partially make it easier to pull out might help.