In this paper, we present the second post-Newtonian solution for the quasi-Keplerian motion of a test particle in the regular Simpson-Visser black-bounce spacetime which has a bounce parameter $a$. The obtained solution is formulated in terms of the orbital energy, angular momentum, and the bounce parameter of the black hole. We explicitly analyze the leading effects of the bounce parameter, which has dimensions of length, on the test particle's orbit, including the periastron advance and orbital period. Then, we apply this model to the precessing motion of OJ 287 and determine the upper limit...
