It's so frustrating, isn't it, @Sarah4039 ! I had to do the same thing recently with an old utility company account, and finally needed to work my way up to someone in customer service who could just change it for me on their end. It took hours.
I really think there is no way to solve it yourself. You'll get the endless loop of verifications being sent to the old number.
So, with Airbnb, I would recommend phoning or using twitter (send a direct message to AirbnbHelp). Just persevere until you get a human who can input your new phone number and who will stay on the line until it shows that it works on your end. I wish you patience and luck!
