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Ad relevance modeling plays a critical role in online advertising systems including Microsoft Bing. To leverage powerful transformers like BERT in this low-latency setting, many existing approaches perform ad-side computations offline. While efficient, these approaches are unable to serve cold start ads, resulting in poor relevance predictions for such ads. This work aims to design a new, low-latency BERT via structured pruning to empower real-time online inference for cold start ads relevance on a CPU platform. Our challenge is that previous methods typically prune all layers of the transformer to a high, uniform sparsity, thereby producing models which cannot achieve satisfactory inference speed with an acceptable accuracy. In this paper, we propose SwiftPruner - an efficient framework that leverages evolution-based search to automatically find the best-performing layer-wise sparse BERT model under the desired latency constraint. Different from existing evolution algorithms that conduct random mutations, we propose a reinforced mutator with a latency-aware multi-objective reward to conduct better mutations for efficiently searching the large space of layer-wise sparse models. Extensive experiments demonstrate that our method consistently achieves higher ROC AUC and lower latency than the uniform sparse baseline and state-of-the-art search methods. Remarkably, under our latency requirement of 1900us on CPU, SwiftPruner achieves a 0.86% higher AUC than the state-of-the-art uniform sparse baseline for BERT-Mini on a large scale real-world dataset. Online A/B testing shows that our model also achieves a significant 11.7% cut in the ratio of defective cold start ads with satisfactory real-time serving latency.