I've never been asked about my travel plans by the airline. But I may check out bus prices just in case. What proof of bus ticket do they expect? Will email confirmation be enough or do the want a print out?
I think Thai Smile and Thai airlines are the only ones that fly out of BKK. The others fly out of Dom Mong so you'll have to take a taxi there. You can confirm who flys where by using Traveloka.com. I personally like Thai Smile. You get 20k for luggage, usually a snack, and a carry-on and personal item for free. All the others charge extra for everything and after all the fees Thai Smile is the cheapest.
then you are correct, a rental will suit you best. The internet is your friend. Search many rental websites to get the best price. Don't accept the first one you see. But one way rentals will probably require you to go with a major rental chain. Good luck!