A BKK taxi will cost about Bht 1,600 plus tolls of Bht 130. (They'll ask for 2,000 but dig in at 1,600) I use a Pattaya based private taxi co who charge Bht 1,200 inc tolls. email:
keak_vt@hotmail.com. Book a few days in advance and they're very reliable.
There is a "van" (private bus) straight to Suvarnabhumi from Jomtien for about 150 Bt but I dont know if they offer one to BKK.
Hope this helps