Couple months ago I came back from a week's vacation to find my whole company turned on its head. A project that another section of the development department had been grinding on for months was suddenly a white-hot-urgent priority, and the whole team was pulled off of what they were working on to churn the thing out. In the meeting that day, the owner of the company asked us to knock out a couple of the pieces that day and the rest the next day and we'd be in good shape.
Six weeks later we finally delivered that thing, after pretty much nonstop work/sleep cycles.
Our metric for "finished" was that the client had no more feedback. New and exciting things would turn up on each version of their feedback (delivered to us by email) that had never turned up before, and every word that they said was instantly part of the spec (justified with the phrase "let's just get it done").
Late one night I had just totally freaking HAD IT with managing bug reports by email and printouts-with-checkmarks. I installed Mantis on our test server and loaded the feedback document I'd just received for my section into it. I set up my manager as a user and let him start getting emails from it as I closed issues.
Within about 6 hours I had the whole team on it. The PM was filtering client emails into Mantis, developers were claiming and working issue lists. Even better, they were able to request clarification and communication inside the system, resulting in a paperless paper trail of details about each item.
The next day they asked me to Tech Lead the rest of the project. It was sort of like being handed a live grenade, but I took it and ran with it. Two weeks later we finally exhausted our client's ability to yank our nose-ring, and put the site into production. Mantis is now how we manage bugs, and might become how we handle feature requests from the beginning of a project.
TL;DR: Install it your own self and start using it for your own stuff. Let it prove its worth on its own.
BTW, this is the same policy I'm following about version control. We use Subversion under a lock-required policy, because my manager doesn't trust file merge. That's fine, but after I check out a SVN project, I immediately make a local git repository of it for my own use in development.