No, Bilbo wasn't trying to use Thorin for his royal bloodline. He never had. He wasn't the type to want power and prestige, and he wasn't the type to use a person. He liked Thorin because of who the Dwarf was as a person, not because of his bloodline. He was glad Thorin knew that, as well.
"I think it must be," he said, once he placed the plates and everything on the table. "I have no recollection of meeting this Aragorn before. He said he met me in Rivendell, and I believe I would have remembered him. I also believe he would have remembered you and Fili and Kili if it had been the only time I remember being in Rivendell."