According to HeirloomRoses.com, KnockoutRoses.net, The American Horticulture Society Encyclopedia of Gardening, and Rayford Clayton Reddell’s The Rose Bible, the best time to transplant roses is during their dormant season, which generally lasts from late winter until early spring. It’s best to wait until the threat of frost has passed, so early spring, from March to April, tends to be a good bet (though this has been an unusual year for weather, with snow in late April). While roses can be transplanted once they’ve started to bloom and grow, it’s more difficult.
Our resources gave a few tips for successful transplantation. Prune back the rose before moving it. When digging up the rose to move it, dig deep enough to get as much of the root ball as possible. Plant it in a well-prepared bed where no roses have previously grown and make sure to water it well after planting and not to fertilize it until it’s established.
For more information, check out Designing with Roses by Tony Lord, Rose Basics by Amanda Beales, and 365 Days of Gardening by Christine Allison.