We got in at 2 am and just hopped in a taxi. I don't think they offered transportation.
I'm not sure sorry. Probably if you ask. Though at Bangkok Airport there are lots of Limo services touting for business.
The sky train takes you right to the hotel. Super convenient.
They don't provide airport pick up. By the way it very convenience for you to travel by MRT and drop at the door step of the hotel.
Get an answer from Asia Hotel Bangkok staff and past guests.