The multi-agent task allocation can be solved in a distributed manner using Consensus-Based Bundle Algorithm (CBBA). Under this distributed auction process, each agent greedily maximizes the global score, which is the difference of the reward and the cost, through an iterative bundle construction and conflict resolution procedure. The distributed algorithm has provable convergence and guarantees 50% optimality if the score function satisfies the condition of diminishing marginal gain (DMG). While the previous work focuses on unconstrained optimization of rewards, this paper aims at applying CBBA to task allocation with budget constraints. Several heuristics were proposed to build the bundle and calculate the bidding scores as improvements to the original CBBA algorithm. We then prove that some of the new score functions are DMG, and therefore guarantees the convergence of the distributed process. We also show that these heuristic extended CBBAs are Pareto efficient; using different heuristic extensions under different scenarios is more efficient than consistently using the same one. To decide which heuristic extension should be used for a given task allocation problem, a graph convolutional neural network (GCN) model is trained to extract and analyze the features of the constrained optimization problem as a graph, and predict the potential performance (i.e., global reward) of different heuristic extensions. Based on the prediction, the best heuristic extension will be selected. Experimental results show that the predicted reward has more than 0.98 correlation with the actual reward and for 70% of time the prediction guided selection picks the best heuristic extension for the budget constrained task allocation problem.