Internet live streaming is widely used in online entertainment and e-commerce, where live advertising is an important marketing tool for anchors. An advertising campaign hopes to maximize the effect (such as conversions) under constraints (such as budget and cost-per-click). The mainstream control of campaigns is auto-bidding, where the performance depends on the decision of the bidding algorithm in each request. The most widely used auto-bidding algorithms include Proportional-Integral-Derivative (PID) control, linear programming (LP), reinforcement learning (RL), etc. Existing methods either do not consider the entire time traffic, or have too high computational complexity. In this paper, the live advertising has high requirements for real-time bidding (second-level control) and faces the difficulty of unknown future traffic. Therefore, we propose a lightweight bidding algorithm Binary Constrained Bidding (BiCB), which neatly combines the optimal bidding formula given by mathematical analysis and the statistical method of future traffic estimation, and obtains good approximation to the optimal result through a low complexity solution. In addition, we complement the form of upper and lower bound constraints for traditional auto-bidding modeling and give theoretical analysis of BiCB. Sufficient offline and online experiments prove BiCB's good performance and low engineering cost.