There aren't too many ways to escape the Bangkok mission area. Namely, there are two of them - one way is by water and the other by land. Unlike in the Marrakech mission, these evacuation points do not require any additional actions other than interacting with them.
Escape by the boat
The motorboat (M6,27) moored to the main quay is an evacuation point which does not require any extra actions (like finding car keys in Marrakech). In order to get to the boat you should leave the building through the main hall and keep walking straight ahead. The motorboat is at the end of the quay.
The emergency exit (M6,12), which leads deeper into the island, is a tad more complicated way out. In order to use it you have to enter the underground tunnel, with access limited to the hotel personnel, and follow it toward the port. At the last cross, you can either turn to the bay or head to the door with the red sign "EMERGENCY EXIT".