In online advertising, once an ad campaign is deployed, the automated bidding system dynamically adjusts the bidding strategy to optimize Cost Per Action (CPA) based on the number of ad conversions. For ads with a long conversion delay, relying solely on the real-time tracked conversion number as a signal for bidding strategy can significantly overestimate the current CPA, leading to conservative bidding strategies. Therefore, it is crucial to predict the number of long-delayed conversions. Nonetheless, it is challenging to predict ad conversion numbers through traditional regression methods due to the wide range of ad conversion numbers. Previous regression works have addressed this challenge by transforming regression problems into bucket classification problems, achieving success in various scenarios. However, specific challenges arise when predicting the number of ad conversions: 1) The integer nature of ad conversion numbers exacerbates the discontinuity issue in one-hot hard labels; 2) The long-tail distribution of ad conversion numbers complicates tail data prediction. In this paper, we propose the Long-Delayed Ad Conversions Prediction model for bidding strategy (LDACP), which consists of two sub-modules. To alleviate the issue of discontinuity in one-hot hard labels, the Bucket Classification Module with label Smoothing method (BCMS) converts one-hot hard labels into non-normalized soft labels, then fits these soft labels by minimizing classification loss and regression loss. To address the challenge of predicting tail data, the Value Regression Module with Proxy labels (VRMP) uses the prediction bias of aggregated pCTCVR as proxy labels. Finally, a Mixture of Experts (MoE) structure integrates the predictions from BCMS and VRMP to obtain the final predicted ad conversion number.