The shuttle bus is a direct service between the two airports and won’t drop passengers anywhere in the route. The buses are air-conditioned and there is a storage area inside for luggage.
A free shuttle bus for passengers to link Bangkok’s two airports SUVARNABHUMI (BKK)  and DON MUANG (DMK).
a very convenient option if you need to transit, I’ve used the shuttle bus many times and it takes 45 to 60 minutes, there is no stop between the airport so it’s the quickest way of public transport between two Bangkok airport

shuttle bus service is operated by Airports of Thailand (AOT)

Document Required

  • passport
  • Flight Ticket / Boarding pass

From Don Muang to Suvarnabhumi airport

the shuttle bus departs from outside the passenger terminal at Don Muang. On arrival at Suvarnabhumi, the bus drops passengers at the departure terminal on the 4th Floor by Gate 5.

From Bangkok Suvarnabhumi to Don Muang airport

The shuttle bus departs from Bangkok Suvarnabhumi on the 2nd Floor (arrivals) outside Door 3. On arrival at Don Muang, the bus drops passengers at the departure terminal

AOT desk will ask you show documents of travel between 72 hours for a free transfer between two Bangkok airport otherwise they wouldn’t allow you 

You need to show flight ticket/boarding pass and passport  ( e-ticket or boarding pass is acceptable  )

time table

The shuttle bus service is operated by Airports of Thailand (AOT) and their target time for the journey between Bangkok Suvarnabhumi and Don Muang is 50 minutes. The times I’ve used the service have been off-peak and in good weather and the journey has always been punctual. If you are traveling during rush-hour and/or in heavy rain, then journey times may be longer.

There are regular departures from 05.00 am in both directions.
See the image below which was taken at Don Mueang airport or the shuttle bus schedule here from AOT.

DISTANCE is Depends on Route
42 min (50.4 km) via Si Rat Expressway ( ทางพิเศษศรีรัช)
47 min (41.0 km) via Ram Inthra Road (ถนน รามอินทรา)
48 min (48.9 km) via Route 9