At the basics - you can use a script task to trigger the test as you would do on a command line. If you're using maven - there's a maven task that allows you to execute the test goal.
After the test - trigger one of the test collecting tasks:
https://confluence.atlassian.com/display/BAMBOO/Configuring+a+test+task (If you're using Maven - it's already done).
That will make Bamboo collect the data and provide you with some metrics.
If you want to save stuff off - configure the Artifacts:
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