The multidisciplinary nature of Web Science is at once its most unique and most challenging characteristic. In this paper, we pose initial questions on how a Web Scientist may explore the topic of cybercrime and cyberwarfare by offering an integrated study of both the social and technical aspects of the phenomena. With this, however, comes a plethora of questions related to methodological practice, data analysis, narrative creation, etc. As such, the following presents initial discussions related to the specific aspects of - objectivity and bias - in science research. The paper includes one example cybercrime case study, which elaborates on the steps taken by the research team to mitigate biases. The paper concludes with additional questions and potential tools/methods to mediate bias for future Web Science studies.