Just because you don't plan to show your kitty doesn't mean you shouldn't register the cat with TICA. It continues the pedigree even if the cat is not going to reproduce. I ordered a 5-generation pedigree when I registered Raiden. There is a great website
http://www.bengalpedigrees.com that has nothing to do with TICA but you can research the ancestry of your bengal -- and you can put your bengal in the database as it probably won't be in there. If the parents aren't in there, you can put that information in from any pedigree papers that you get. From there, you can do up to a 15-generation pedigree instantly which will be LONG but bring up all the kitties and hopefully at least a few ALCs.
I never expected to get papers for Raiden as the previous owner GAVE him to me. I was never going to ask for them. But he offered them and I took them and registered Raiden. Happy I did! I love the laminated 5-generation pedigree that cost me $50, I think. Well worth it in my opinion.