This paper joins a growing body of work within ICTD and related fields studying the privacy challenges in the Global South. While most of the existing work in this area has focused on uses of technology in personal and home settings, a large part of computing in the Global South centers around public places, such as commercial Digital Service Centers (DSCs). In this paper, we present the findings from a six-month-long ethnography studying 19 Digital Service Centers in Dhaka, Bangladesh. We find that infrastructural limitations, local power politics, lack of knowledge, and insufficient protection mechanisms lead to privacy vulnerabilities for the customers of these centers. We apply the lens of informal markets to analyze these vulnerabilities and connect our findings to the broader concerns of ICTD around development, ethics, and postcolonial computing and discuss potential design and policy implications around these issues.