In tree-based genetic programming (GP) with sub-tree crossover, the parent contributing the root portion of the tree (the root parent) often contributes more to the semantics of the resulting child than the non-root parent. Previous research demonstrated that when the root parent had greater fitness than the non-root parent, the fitness of the child tended to be better than if the reverse were true. Here we explore the significance of that asymmetry by introducing the notion of crossover bias, where we bias the system in favor of having the more fit parent as the root parent. In this paper we apply crossover bias to several problems. In most cases we found that crossover bias either improved performance or had no impact. We also found that the effectiveness of crossover bias is dependent on the problem, and significantly dependent on other parameter choices. While this work focuses specifically on sub-tree crossover in tree-based GP, artificial and biological evolutionary systems often have substantial asymmetries, many of which remain understudied. This work suggests that there is value in further exploration of the impacts of these asymmetries.