Jessica, you need to send prototypes of your clothes to a factory in China to reproduce and quote. You can go to alibaba.com, globalsources.com and made-in-china.com to search for clothing manufacturers in China. You will find hundreds. Look through their product pictures for the factories that are producing items similar to yours. Look for the suppliers that are "certified" or have "gold stars" or whatever the different sites use to differentiate the "best" suppliers from the rest of the pack. Note that using these web sites is risky and there's no guarantee that what you see is what you get. Your other, better option for finding a supplier is to invest in a trip to China to attend a textiles/clothing trade show where you can meet suppliers face to face and show them your prototypes. Globalsources.com has good information on shows taking place in China.
Doing this via the internet and emails is not recommended, but you can try and you might even succeed. First email images of your prototypes along with detailed descriptions of the materials to several suppliers and ask them what their MOQs would be (minimum order quantities).
After you have two or three suppliers you think are capable, enthusiastic, cooperative and interested in working with you, you can send them your prototypes and have them quote and reproduce them to demonstrate their capability. Note that the most challenging aspect of this will be getting the supplier to match your material. They will use whatever materials are readily available over there. Like you suggested, after you send them your prototypes you can ask them to send you swatches of materials they can procure easily. In many cases the only way they can match your materials exactly is by having them custom-made, which will be costly because the minimums are usually something like 1000 yards.
If all goes well and you find yourself with a supplier that is willing and able to do the job, then comes the hard part: how are you going to sell your clothes in sufficient quantities to keep the supplier interested in supporting you? In my opinion, if you have the sales and distribution, then getting the product made in China is the easy part. You should not be thinking about how to make your clothes in China unless you are already selling thousands of pieces of your clothes per month. You should find a way to get your clothes made in the U.S. first, even if you are just breaking even. You need to first develop a customer base and get some demand going, THEN you can start worrying about reducing your costs by moving production to China. Good luck, Hank