May is a good time, in general, although crowds will build in later May, especially in touristy places like Gordes and Les Baux en Provence.
The key question is whether you will have a car? And how serious of a cyclist are you?
The Luberon is one area that might interest you. There are a number of bike rental shops in the various towns/villages, including a couple in Bonnieux (example). There is a flat trail in the center of the valley but also mountain biking opportunities.
For a biking centric tour, I would not stay in someplace as large as Aix or Montpellier. Travel wise, you might just consider fllying to Paris and taking the TGV down to Avignon. From there, you could go to a smaller town like St. Remy or a village in the Luberon (Bonniuex, Menerbes, Roussillon, St Saturnin, etc). I was also just in Orange recently and it is lovely and off the traditional tourist routes (unless you are Dutch) and villages like Chateauneuf-du-Pape, Vaison la Romaine and Gigondas are very great.