The circle of dirt should be as wide as the widest part of the bush. This is known as the drip line and is true for all woody shrubs and trees. Grass and other invasive plants prevent air and water from getting to the roots. Even tho roses have a primary tap root, the feeder roots still fan out.

You don't want to plant parsley beneath or near a rose because the sun and water needs are too different. Parsley likes part shade and a lot of water. Roses want full sun and deep but less frequent waterings (once or twice a week) in well-drained soil. The soil closer to the surface should be just be cool-moist but not wet.

If you want to plant herbs near a rose, choose the woody Mediterranean herbs like thyme, oregano, etc. chives are good to plant because they help prevent insects.

And for future reference, the space around the rose should extend out to the rose's anticipated mature width and a bit farther. An immature rose may be only 2-3 ft wide, for instance, but by year four, 4-6 ft wide.

Kate

Check out the mature width on helpmefind.com and plant accordingly. If the mature width of the roses you are planting is 3 feet, that means the rosebush will grow out 1 1/2 feet each way from it's center.
By planting them three feet apart the bushes will touch when mature. Planting them 42 inches apart means there should be 12 inches of space between the bushes when mature. The mature size is influenced by your growing zone, how you fertilize, how you water, and how you prune. If you want them to grow together late in the season you can plant them closer together or if you want them to be distinctly separated you can plant then farther apart. When room is at a premium, you can plant them closer and keep them pruned back more.
At one time I had 550 bushes on a lot 165'by 60' My roses were planted 18 inches apart. by summers end, they were terribly growing into each other but the effect was stunning. I could get away with it because I sprayed and the bushes experienced a lot of winter dieback resulting in much smaller bushes each spring as a result of the severe pruning required.
In my larger lot here where I live now, the bushes are 3-4 feet apart or more depending on their mature size. I have less disease pressure due to better air circulation around each bush. That's something else to take into consideration.

I thought that Parsley was a companion plant to roses and that they were even supposed to enhance their aroma.

I've never heard that about parsley, and I don't know about the enhancing aroma bit--sounds a bit like an old wives' tale. Perhaps in some rainy place like England or Oregon it would work with some kinds of roses. But I wouldn't try it.

In my gardening magazines, there is no space between the roses and the other plants, everything grows together, even in the pots they recommend planting something else together with the roses. I am very confused now. Which is better?? Thanks for starting this discussion, it is very interesting.

OoPs, I failed to see that you were referring to the space around a bush if you wanted to plant companion plants around them.
In that case, it's pretty much up to you. Anything close to the bush will take nutrients and moisture away from it so you'll have to fertilize and water more often.
You'll have a bit of a problem keeping it weeded. You'll not be able to scratch in fertilizeraround the bush if you leave little or no room to do that. I prefer to keep everything but roses out of my rose beds.