Fairlight is served by the 101 bus serviced service. The timetable is available here.
Taxis do serve Fairlight, but be careful as some charge to come out to you.
Jempson's Hail & Ride Bus Service
Jempson's run a weekly bus service from Fairlight to their store in Peasmarsh. There is a nominal charge of £1 per customer (return journey) for this service. If you live between stops and are outside your house at the appropriate time just put up your hand when you see the bus coming and it will pick you up.
The service is in Fairlight at around 09:25 each Friday and will get you back at about 12:30.
Full details can be found on the Jempson's Web Site.
Tesco's Bus Service
Tesco's free bus service to Churchwood Drive leaves from the bus stop by the Cove Public House (by Estate Agents) at 09:45 on Fridays and arrive at Tescos at 10:20. You have 2 hours for shopping before the bus departs at 12:25, arriving back in Fairlight at 12:55. The bus timetable can be viewed or downloaded here (look for Service C in the timetable).
Hastings Community Transport (Dial-a-Ride)
Door to door wheelchair accessible transport service for people of all ages who find it difficult or impossible to use public transport. The service operates Monday to Friday within the borough of Hastings and St Leonards. Also now covers Fairlight, Guestling, Pett, Westfield, Three Oaks. There's a leaflet about the service available here.