If Winnats is too busy (most summer weekends), then taking the old Mam Tor road can be a very pleasant alternative. It's not only traffic free, but was built as a less steep variation to Winnats Pass for the stage coaches on the toll road.
You will have hop off on a road bike a couple of times, but apart from that, it's all good tarmac.
The circuit up Mam Tor and Down Winnats is great.