Context: Security bug reports are reports from bug tracking systems that include descriptions and resolutions of security vulnerabilities that occur in software projects. Researchers use security bug reports to conduct research related to software vulnerabilities. A mapping study of publications that use security bug reports can inform researchers on (i) the research topics that have been investigated, and (ii) potential research avenues in the field of software vulnerabilities. Objective: The objective of this paper is to help researchers identify research gaps related to software vulnerabilities by conducting a systematic mapping study of research publications that use security bug reports. Method: We perform a systematic mapping study of research that use security bug reports for software vulnerability research by searching five scholar databases: (i) IEEE Xplore, (ii) ACM Digital Library, (iii) ScienceDirect, (iv) Wiley Online Library, and (v) Springer Link. From the five scholar databases, we select 46 publications that use security bug reports by systematically applying inclusion and exclusion criteria. Using qualitative analysis, we identify research topics investigated in our collected set of publications. Results: We identify three research topics that are investigated in our set of 46 publications. The three topics are: (i) vulnerability classification; (ii) vulnerability report summarization; and (iii) vulnerability dataset construction. Of the studied 46 publications, 42 publications focus on vulnerability classification. Conclusion: Findings from our mapping study can be leveraged to identify research opportunities in the domains of software vulnerability classification and automated vulnerability repair techniques.