We got the buggy from our condo to drop us off at the top of Tesco-Lotus and then walked the short distance to the main Sukhumvit road to hail down a taxi driver. He agreed to take us to the airport and we agreed to use the Expressway which is quicker but you need to pay tolls.
Two tolls later (THB 40 and THB 25) we were soon on a new stretch of smooth motorway which knocked the entire journey to under half an hour. Cost for the trip, THB 223 (+ the THB 65 toll fees). Champion.