Hi Greg,
Typically the camera could have a target, and the bicycle you like to keep sharp is the target. With Motion Blur enabled, that should be all.
You wrote the “impression of”, which feels like you have a fixed background and that should be just blurred, which could be done in Photoshop. The Blur filter is called Motion blur, and you need to set the direction and strength.
I have attached an image from my time shooting German Championship races on the Hockenheim Ring. I used a longer lens and moved with our Driver.
It was in the 180ยบ curve, so moving with the subject was easy to keep it in focus.
Why do I show this? As it shows clearly, the wheels have blurred as well. Some bicycle wheels have carbon rims, which have thicker elements. They would show up. Which can also be blurred before. (Photoshop radial)
Al the best