Jonathan, do the following, pick off all the affected leaves and any left on the ground and any detritus around the rose. If this means stripping the rose of foliage do it. Spray the whole rose, including flowers with fungicide and the ground around the rose. Feed the rose and mulch heavily with compost or well rotted farmyard manure, then water well.
Even if the rose looks bare which it will don't worry as new growth will appear within a few weeks. It works and I have given this advice frequently on this forum more times than I care to mention. It does work so don't worry about it looking bare.
If infection is present on any new growth do it again.
It's been a bad year for black spot as we had little or no frost last winter to kill the spores.
I don't know if you refreshed the soil when you planted the new rose, but the addition of mychorizal fungi to the planting hole would have helped. Some recommend planting inside a cardboard box with fresh soil inside, but I find the fungi do the job equally as well along with plenty of organic matter added. If you didn't I'd replant it in November using the above to give it the best chance for next year.
Next year spray with fungicide as soon as the first new growth appears to keep on top of any possible infection.