Suvarnabhumi - Ayutthaya

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Is there a direct bus from the airport to Ayutthaya, maybe leaving from the little bus terminal located just outside the airport?

Alternatively, is there some sort of bigger taxi (there is 7 of us plus baggage)?

Alternatively, do regular taxis (that is, two of them for all of us) go flat rate or meter on that route? How much?

I know of some non-convenient ways to get there (taxi/bus to Mochit + bus, taxi/bus to Hua Lamphong + train, etc...), I am looking for more convenient ways (possibly not too expensive).

Thanks

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So I ended up in page 2 with no reply. Nobody knows?

Thanks