Agentic AI serving converts monolithic LLM-based inference to autonomous problem-solvers that can plan, call tools, perform reasoning, and adapt on the fly. Due to diverse task execution need, such serving heavily rely on heterogeneous CPU-GPU systems with majority of the external tools responsible for agentic capability, either run on or are orchestrated by the CPU. Towards having a deeper understanding of its role, this paper aims to characterize and analyze the system bottlenecks introduced by agentic AI workloads from a largely overlooked CPU-centric perspective. We first present a compile-time characterization of agentic AI execution and choose representative workloads to capture the algorithmic diversity. We then perform runtime characterization of the representative workloads analyzing the end-to-end latency and throughput on two different hardware systems to isolate respective architectural bottlenecks. Based on the insights on the bottlenecks, we finally present two scheduling optimizations, namely, 1. CPU-Aware Overlapped Micro-Batching (COMB) and 2. Mixed Agentic Scheduling (MAS) on homogeneous and heterogeneous agentic workloads, respectively. In specific, these methods optimize for improved CPU-GPU concurrent utilization while reducing skewed resource allocation for heterogeneous execution. Experimental evaluations on the two hardware systems demonstrate the efficacy of COMB in yielding up to 1.7x lower P50 latency in standalone homogeneous workload execution and up to 3.9x/1.8x lower service/total latency under homogeneous open-loop load. Additionally, for heterogeneous open-loop load, MAS can reduce the total latency for minority request-type by up to 2.37x/2.49x at P50/P90 percentile.