Classifying encrypted sensor traffic is critical for the security and management of Internet of Things networks, particularly in Mobile Edge Computing (MEC) environments. Existing methods often require extensive task-specific labeled data to adapt to emerging traffic categories and may also fail to distinguish intrinsic traffic behaviors from patterns introduced by shared communication libraries, which can degrade classification accuracy under distribution shifts. To address these issues, we propose CDTF, a contrastive dual-task framework for transferable and few-shot traffic representation learning. CDTF adopts a hybrid pre-training strategy that jointly optimizes supervised triplet pretraining (STP) and self-supervised dynamic burst masking (DBM). STP uses base-class labels as structural anchors to explicitly constrain distance relationships by aligning intra-class samples and separating inter-class samples, thereby mitigating interference from shared network components. DBM models global semantic structures and enhances the robustness of traffic representations against network noise and distribution shifts. By learning discriminative and contextual representations in a shared embedding space via these two tasks, CDTF can rapidly adapt to novel categories through lightweight fine-tuning, thereby substantially reducing the reliance on large-scale fine-grained supervision in downstream tasks. Experimental results across seven public and two custom datasets, across diverse environments, show that the proposed framework outperforms state-of-the-art methods. Under the few-shot setting, CDTF improves Precision by 4.61 percentage points over the strongest baseline, with statistical significance confirmed by a paired t-test ($p<0.05$).