The iOS 8 Airplay menu is a slightly different. After selecting your device, you may have to open the Airplay menu again. You may also need to scroll the list after selecting your computer in order to find the mirroring switch. It may not look like the menu scrolls, but sliding your finger will likely move the list.
Here is a link to a video showing this: https://www.youtube.com/watch?v=ER2M9TGLNY0&feature=youtu.be