In Tolkien’s Middle-earth; was Rhun based primarily on Asia? I think there are Bilbo references to this in The Hobbit, but I do not know certainly. Does anybody know the answer of this topic?
We don't know that much about Rhûn but I think it's safe to say that it is Middle-earth's equivalent to central Asia. The Wainriders seem to be inspired by cultures like Scythians and how they fight wars (which was discussed in the comments under the question).
Also, In the early drafts of The Hobbit Bilbo does mention China existing in the east:
to the last desert in the East and fight the Wild Wireworms of the Chinese
Source: J.R.R. Tolkien, John D. Rateliff (ed.), The History of The Hobbit, Mr. Baggins, The First Phase, "The Bladorthin Typescript", p. 40
There was an interview of Tolkien to clarify the topic.
Excerpts from: Henry Resnick, “An Interview with Tolkien [March 2, 1966],” Niekas No. 18 (Late Spring 1967).
(“Rhun is the Elvish word for ‘east.’ Asia, China, Japan, and all the things which people in the west regard as far away. And south of Harad is Africa, the hot countries.” (Resnick, “An Interview,” 41))