There is growing awareness of the need for mathematics and computing to quantitatively understand the complex dynamics and feedbacks in the life sciences. Although several institutions and research groups are conducting pioneering multidisciplinary research, communication and education across fields remain a bottleneck. The opportunity is ripe for using education research-supported mechanisms of cross-disciplinary training at the intersection of mathematics, computation, and biology. This case study uses the computational apprenticeship theoretical framework to describe the efforts of a computational biology lab to rapidly prototype, test, and refine a mentorship infrastructure for undergraduate research experiences. We describe the challenges, benefits, and lessons learned, as well as the utility of the computational apprenticeship framework in supporting computational/math students learning and contributing to biology, and biologists in learning computational methods. We also explore implications for undergraduate classroom instruction and cross-disciplinary scientific communication.