Yes, only a registered business entity in China is capable of invoicing or receiving payment in renminbi. A wholly-owned foreign entity (WOFE) is the most common form of business entity in China and the easiest to establish. That said, the time is still lengthy compared to the week it takes to set up a corporate entity in the state of Delaware. Expect this process to be anywhere from four to six months and have a number of unique requirements. Of particular note is the legal requirement that, prior to receiving a business license and early on in the application process, a long-term lease of at least one year must be signed for the rental of an office in the Chinese city in which the WOFE is to be established. Without this, an application won't be processed or approved.
Be advised that China is the largest producer and supplier of all types of bathroom products in the world. Certainly, a high quality foreign shower product may gain a small market share in China, but there are risks involved in terms of protecting your intellectual property and finding a distributor. You should protect your trademark and design prior to coming to China as China is a first-to-file country, meaning that it's possible that your trademark could be filed by a Chinese entity. As for distributors, there are tens of thousands involved in the bathroom product sector, mostly located in Guangdong province, and perhaps a distributor that deals with high-end showers would be willing to carry your product.