In the present paper, we give the notion of $k$-type bi-null Cartan slant helices in $\mathbb{R}_{2}^{6}$, where $k\in \left \{ 1,2,3,4,5,6\right \} $. We give the necessary and sufficient conditions for bi-null Cartan curves to be $k$-type slant helices in terms of their curvature functions.