In modern computing systems, jobs' resource requirements often vary over time. Accounting for this temporal variability during job scheduling is essential for meeting performance goals. However, theoretical understanding on how to schedule jobs with time-varying resource requirements is limited. Motivated by this gap, we propose a \emph{new setting} of the stochastic bin-packing problem in service systems that allows for \emph{time-varying} job resource requirements, also referred to as `item sizes' in traditional bin-packing terms. In this setting, a job or `item' must be dispatched to a server or `bin' upon arrival. Its resource requirement may vary over time while in service, following a Markovian assumption. Once the job's service is complete, it departs from the system. Our goal is to minimize the expected number of active servers, or `non-empty bins', in steady state. Under our problem formulation, we develop a job dispatch policy, named Join-Reqesting-Server (JRS). Broadly, JRS lets each server independently evaluate its current job configuration and decide whether to accept additional jobs, balancing the competing objectives of maximizing throughput and minimizing the risk of resource capacity overruns. The JRS dispatcher then utilizes these individual evaluations to decide which server to dispatch each arriving job to. The theoretical performance guarantee of JRS is in the asymptotic regime where the job arrival rate scales large linearly with respect to a scaling factor $r$. We show that JRS achieves an additive optimality gap of $O(\sqrt{r})$ in the objective value, where the optimal objective value is $Θ(r)$. When specialized to constant job resource requirements, our result improves upon the state-of-the-art $o(r)$ optimality gap. Our technical approach highlights a novel policy conversion framework that reduces the policy design problem into a single-server problem.