In blockchain systems, the design of transaction fee mechanisms is essential for stability and satisfactory for both miners and users. A recent work has proven the impossibility of collusion-proof mechanisms with non-zero miner revenue which is Dominate-Strategy-Incentive-Compatible (DSIC) for users. In our work, we relax the DSIC requirement for users to Bayesian-Nash-Incentive-Compatibility (BNIC), and design a so-called soft second-price mechanism to ensure a form of collusion-proofness with an asymptotic constant-factor approximation of optimal miner revenue. Our result breaks the zero-revenue barrier while preserving reasonable truthfulness and collusion-proof properties.