Blur out private or sensitive info
First off, invoke Shake to start the reporting process. Tap the Blur icon located in the bottom menu of your screen and start sliding over the parts of the screenshot you want to blur out, until you're satisfied with the result.
That's it, all done. You can now submit the bug and the blurred out sections won't be visible to anyone.
Or, remove the screenshot altogether
There's an alternative to blurring — if you don't want to submit your screenshot at all, you can remove it altogether:
Go to the Wrap-up screen
Notice your screenshot in the Attachments section
Tap X in the screenshot's top-right corner to delete it.
This way, you will report a bug without a screenshot.