No, you are not missing anything. The Bootstrapper is considered an out of band mechanism to support ClickOnce deployments, not an integral part of them. ClickOnce deployments are targeted for least privilege users, the Bootstrapper almost always requires admin privilege. In your case, you would have to send a notification to the user to rerun the bootstrapper through a link to get the new prerequisite in place before applying the update through ClickOnce.
Not pretty, but really your only choice short of finding a way to get that other stuff on the client machine as part of the ClickOnce install. You could potentially deploy the MSI with the ClickOnce update and run it from your app on startup (checking the ApplicationDeployment.IsFirstRun flag), but that would assume your users always have permissions to do that and that your app can at least start up and launch the msi (through a Process.Start call) and wait until the install is complete.