Well the best way to do this is to approach these people when they check in, rather than on their way out. After their stay is over, customers will just be eager to get on their way and they would not want to be bothered.
I would explain to them that it would help the hotel (at which they are about to stay) to improve its service if they would agree to take the survey after their stay is over. Making them aware in advance of their stay that the survey will be done, will also help them notice the details of the service given to them during their stay.
It would be great if you were allowed to give them a small incentive, such as a 5% discount or complimentary drinks or something, but I assume you are not budgeted for this. Instead, maybe you could tell them that if they do the survey, they will be placed on a list of preferred or special customers who will be notified by mail or email of any specials that the hotel might feature in the future.