I am afraid it is impossible for you to get the invitation letter if you book everything yourself. As I know, the local travel agency will offer you the letter only if you book and pay for the itinerary with them.

You can send your hotel confirmation letter plus your airline ticket confirmation to get your visa to visit China. I just came back from China last week, I bought everything without a tour group and was able to get the visa by sending them the confirmation letter from the hotel and the airline. Hope this help. I did use a visa service to make sure that my visa application was correct.