Every Process Template makes certain assumption about how you structure your work. You can either work within those constraints or start customizing the Process Template.
For example the Agile PT only includes User Stories in the backlog, and assumes all work will have a User Story with related Tasks (bugs are the worst here, because to conform with the PT assumptions it expects you to create a Bug, then create a linked User Story to plan the work, then create Tasks to track the work).
The Scrum PT in 2012 is better as it includes both User Stories and Bugs in the backlog.
If none of those meets your needs you can always start customizing the Process Template (by editing the Categories.xml and CommonConfiguration.xml) in the Process Template. Here's a blog post by Colin about customizing the Agile PT to include Bugs in the Backlog: http://www.colinsalmcorner.com/2013/01/subtle-msf-agile-enhancement-adding.html