Using the notion of bipolar-valued fuzzy sets, the concepts of bipolar fuzzy (weak, $s$-weak, strong) hyper BCK-ideals are introduced, and their relations are discussed in \cite{IJFS080910}. Further properties are investigated in this article. We show that if $\Phi=(H;\mu_{\Phi}^P, \mu_{\Phi}^N)$ is a bipolar fuzzy (weak, strong) hyper $BCK$-ideal of a hyper $BCK$-algebra $H,$ then the set \[\text{$I:=\{x\in H\mid \mu_{\Phi}^P(x)=\mu_{\Phi}^P(0),$ \; $\mu_{\Phi}^N(x)=\mu_{\Phi}^N(0)\}$}.\] is a (weak, strong) hyper $BCK$-ideal of $H,$ but not converse by providing examples. Using a collection of ordered pairs of (weak, strong) hyper $BCK$-ideals of a hyper $BCK$-algebra $H,$ a bipolar fuzzy (weak, strong) hyper $BCK$-ideal of $H$ is established.