View bounces when sending through general email (not CiviMail)
Found my own answer. Our bounces@... address is set up as a catch-all, so bounces (or other badly addressed email) come to it, but CiviMail only processes bounces from emails sent through that component. Other emails are sitting in the inbox of the bounces@ account, waiting to be read, or forwarded through judicious use of a filter.

Leaving this question for posterity.