I have been doing some research into this as well, I think it would be generally better to approach people about "building a pond" instead of a "natural swimming pool, as that seems to add the idea of a premium kind of thing. that said, machines and experienced operators are very expensive and there is no getting around that. depending on your soil and everything (which will require some testing) you may not exactly need to line it at all, just have an experienced
pond builder that knows what they are doing and have the appropriate siting and soil tests. I don't have
experience lining ponds with bentonite, but i have experimented with it a little bit, here's one thing to consider: if you don't entirely cover the area that's lined it will remain incredibly slick forever. It is very slippery. so keep that in mind. Are you planning on having some kind of filtration for this or will it be more of a static pool? if so that changes how it's designed a little bit. Here are a few videos that might have some good relevant information for you:
https://www.youtube.com/watch?v=7N4ftMi_I1I <--this guy in the second
video might be worth contacting, I know he did a nice pond in tennesee which you will see in the video there, he will have a lot more practical guidance than I can offer and he might even be kicking around on the forums here somewhere... also I hear
sepp holzer has a book on pond building but I have not sought it out yet.