Auction-based Federated Learning (AFL) is a burgeoning research area. However, existing bidding strategies for AFL data consumers (DCs) primarily focus on maximizing expected accumulated utility, disregarding the more complex goal of revenue maximization. They also only consider winning bids, leading to biased estimates by overlooking information from losing bids. To address these issues, we propose a Bias-free Revenue-maximizing Federated bidding strategy for DCs in AFL (BR-FEDBIDDER). Our theoretical exploration of the relationships between Return on Investment (ROI), bid costs, and utility, and their impact on overall revenue underscores the complexity of maximizing revenue solely by prioritizing ROI enhancement. Leveraging these insights, BR-FEDBIDDER optimizes bid costs with any given ROI constraint. In addition, we incorporate an auxiliary task of winning probability estimation into the framework to achieve bias-free learning by leveraging bid records from historical bid requests, including both winning and losing ones. Extensive experiments on six widely used benchmark datasets show that BR-FEDBIDDER outperforms eight state-of-the-art methods, surpassing the best-performing baseline by 5.66%, 6.08% and 2.44% in terms of the total revenue, ROI, and test accuracy of the resulting FL models, respectively.