Roses need full sun to perform their best. I would not plant them closer than the outer branch spread of the tree for the sake of keeping them in bright sunlight. Otherwise their blooming will be dramatically reduced. Drake elms do cast a light shade, especially near the periphery of the tree, but I think it will nevertheless be a bit too much for your roses.
The roots of the tree are a secondary concern. From the standpoint of the roots, whether you plant them 10 feet from the trunk or just past the drip line, the tree roots will find and proliferate in the rose bed. Periodic (yearly?) root cutting by trenching or use of a sharp shovel to vertically cut down into the soil to sever the encroaching tree roots will help reduce the competition for the roses. These cuts should go down 10-12" Deep to be most effective.
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