The first flights get going on the 3 May and the prices look pretty reasonable - I've just randomly selected London Ajaccio return for a week departing on Thursday the 7 June and that comes in at £104.32. This includes a 23kg checked bag, a 12kg cabin bag, a free drink, snack and newspaper. Very good value!
The cost of bike carriage is an expensive extra and adds around £135 (Easyjet charge £84 for example) to your air fare bringing the total to £240 return. However, the basic airfare is such good value that the total cost is competitive compared to say a week in Majorca with your bike at the same time of year.
Alternatively, you can rent a bike by the day from Bastia, Ajaccio, Calvi and Ile Rousse. Click here for rental shops.