  We prove a bi-ordered version of Rivas' result for free products of
left-order groups. Namely, we show that a free product of bi-ordered groups
does not admit isolated bi-ordering. Our method relies on the dynamical
realization of bi-ordered groups. We also show that the natural action of the
automorphism group $Aut(F_2)$ on $F_2$ does not have dense orbits.
