If all else fails, one of you can run in to the front desk of your hotel and get some change.

About large bills in Thailand: the largest denomination is 1000 baht, approximately US$30. By world standards, that's not a terribly large banknote. With fare and tolls running about 300-400 baht from Suvarnabhumi to major hotels, you won't need a great deal of change. That said, 1000-baht note is a big note for a lot of Thais. Cab drivers should be able to make change, 7-11's too, but street vendors might give you grief.

glob99's suggestion is the best and most efficient. Almost all cab drivers will require you to pay the toll during the ride anyway, so break the 1000-baht note at the tollbooth.