The best time to transplant rose bushes is when they are dormant (not actively growing). Transplanting in the autumn or winter means your plant will put on new growth in time for spring.
In cool temperatures a rose bush plant isn't actively growing. It doesn't mind being uprooted, because its water and nutritional needs are less.
Roses can be pruned heavily while dormant. Moving them at this time means they will be lighter and have fewer thorns, making them easier to handle.
Roses are not temperamental plants. In fact, they are quite resilient. They respond very well to being relocated if given adequate water, light and nutrition.