Given a simple finite graph $G=(V(G), E(G))$, a vertex subset $D\subseteq V(G)$ is a distance $k$-dominating set if every vertex $v\in V(G)-D$ lies within distance $k$ of some vertex in $D$. The distance $k$-domination number $\gamma_k(G)$ is the cardinality of a minimum distance $k$-dominating set. The distance k-bondage number $b_k(G)$ is the size of a minimum edge set B suchthat $\gamma_k(G-B)>\gamma_k(G)$. In this paper, we establish upper bounds on $b_k(G)$ in respect to degree sums and exact values of a k-distance bondage number for common graph classes. Our results generalize previous bounds by incorporating distance-based domination constraints. We also introduce a refined bound in respect to the number of internally disjoint paths. These findings contribute to the broader study of domination and bondage parameters in restricted graph classes and provide insights into combin atorial optimization.