There have been some pretty negative reviews in the Suvarnabhumi sub-forum on Thaivisa dot com. Infrequent service (1 hour+ wait) and lengthy trips (taking 1 hours plus). Given that three of the four bus routes involve expressways (the Silom route uses the Bangna-Trat road/expressway/tollway) it seems like they should be quicker? I guess, depending on my destination, I'd take either a taxi or the 35 baht bus? With lots of bags it'd be a taxi of course.
More bus details:
Bus
The airport operates 4 airport express bus routes to downtown Bangkok. The buses are air-conditioned with ample luggage space. The fare is 150 baht for the entire route. Passengers can get on the bus on the first floor of the terminal. The four routes are as follows:
AE1 Suvarnabhumi-Silom Rd. (by expressway)
AE2 Suvarnabhumi-Khao San Rd.(by expressway)
AE3 Suvarnabhumi-Central World via Sukhumvit Rd.
AE4 Suvarnabhumi-Hua Lamphong (central Bangkok Railway Station) via Victory Monument(by expressway)
Additionally, 12 city bus routes operated by Bangkok Mass Transit Authority (BMTA) serve the airport's dedicated bus terminal. City buses offer a cheaper alternative of Bt35 flat fare, compared with the airport express bus, but passengers must take a shuttle bus to the public transportation center's bus terminal before they can board the bus. The 12 routes are as follows:
549 Suvarnabhumi-Minburi-Bangkapi via Seri Thai Rd.
550 Suvarnabhumi-Happy Land
551 Suvarnabhumi-Victory Monument (by expressway)
552 Suvarnabhumi-Khlong Toei (Customs Dept.) via Onnut BTS station
552A Suvarnabhumi-Samut Prakarn (Praeksa Garage)
553 Suvarnabhumi-Samut Prakarn (Crocodile Farm Garage)
554 Suvarnabhumi-Rangsit via Don Mueang and Ram Indra Rd. (by expressway)
555 Suvarnabhumi-Rangsit via Don Mueang and Central Plaza LadPhrao (by expressway)
556 Suvarnabhumi-Bangkok Southern Bus Terminal via Democracy Monument and Khaosan Rd.(by expressway)
557 Suvarnabhumi-Wong Wian Yai (The Great Circle)
558 Suvarnabhumi-Central Plaza Rama II
559 Suvarnabhumi-Future Park Rangsit via Dream World (by expressway)
There are also direct long-distance services to Pattaya and Nong Khai operated by the Transport Company.
All of the city buses and inter-city buses are air-conditioned