Based on this answer the model for the TFS 11 burndown chart is for tasks that a children to stories.
How can I display a burndown chart of the currently opened bugs during a sprint without having to create subordinate work items for them?
The way it is intended is that you add tasks as children of the bug as soon as the bug is added to a sprint. These tasks will drive the burndown. This is the same for Product Backlog Items and it is very simple through the web ui. The estimation data in the bug itself will be represented in the release burndown.
Should you want the bug itself to function as a task, you can either:
You should also keep in mind that bugs found for work that was done in a previous sprint should only be picked up in the current sprint during the sprint planning meeting, or when it is critical to fix it as part of the current sprint. In the first case, treat it as just any other PBI and break it down into tasks. In the second case, go fix it immediately, don't bother about the burndown, the bug is critical and should be fixed now.