How are the Dhuhr and Asr prayers performed, and is it permissible to combine and shorten them, when traveling by bus from an oil field to the airport after or before the Dhuhr prayer, with the possibility of waiting for the flight until after the Asr prayer?

If you depart from the oil field, you are permitted to avail yourselves of the concessions for travel, which include combining the Dhuhr and Asr prayers with Qasr (shortening). You may combine them as a delayed or an advanced combination. This combining and all other travel concessions cease upon your arrival at your place of residence.