Auto-bidding is crucial in facilitating online advertising by automatically providing bids for advertisers. While previous work has made great efforts to model bidding environments for better ad performance, it has limitations in generalizability across environments since these models are typically tailored for specific bidding scenarios. To this end, we approach the scenario-independent principles through a unified function that estimates the achieved effect under specific bids, such as budget consumption, gross merchandise volume (GMV), page views, etc. Then, we propose a bidding foundation model Bid2X to learn this fundamental function from data in various scenarios. Our Bid2X is built over uniform series embeddings that encode heterogeneous data through tailored embedding methods. To capture complex inter-variable and dynamic temporal dependencies in bidding data, we propose two attention mechanisms separately treating embeddings of different variables and embeddings at different times as attention tokens for representation learning. On top of the learned variable and temporal representations, a variable-aware fusion module is used to perform adaptive bidding outcome prediction. To model the unique bidding data distribution, we devise a zero-inflated projection module to incorporate the estimated non-zero probability into its value prediction, which makes up a joint optimization objective containing classification and regression. The objective is proven to converge to the zero-inflated distribution. Our model has been deployed on the ad platform in Taobao, one of the world's largest e-commerce platforms. Offline evaluation on eight datasets exhibits Bid2X's superiority compared to various baselines and its generality across different scenarios. Bid2X increased GMV by 4.65% and ROI by 2.44% in online A/B tests, paving the way for bidding foundation model in computational advertising.