Being a programmer working on an already critical (or least, important) task, should not let yourself deviate by trying to develop something that is already available in the market (open source or commercial).
You will now try to create a bug tracking system to keep track of the bug tracking system that you use to track bugs in your core development.
First:
1. Choose the platform your bug system would run on (Java, PHP, Windows, Linux etc.)
2. Try finding open source tools that are available (by open source, I mean both commercial and free tools) on the platform you chose
3. Spend minimum time to try to customize to your need. If possible, don't waste time in customising at all
For an enterprise development team, we started using JIRA. We wanted some extra reports, SSO login, etc. JIRA was capable of it, and we could extend it using the already available plugin. Since the code was given part of paid-support, we only spent minimal time on writing the custom plugin for login.