Maven: `Unknown packaging: bundle` error from a dependency packaging as bundle

I tried adding the maven-bundle-plugin to my own POM file's tag, but that won't fix it (and why should it? I'd think that a dependency's config shouldn't affect my pom?

And you are right : it is not the maven-bundle-plugin as a dependency that you need to add to make the bundle package usable in your build.
What you need is adding the maven-bundle-plugin as a plugin to enhance the default Maven lifecycle such as :

<build>
  <plugins>
     <plugin>
        <groupId>org.apache.felix</groupId>
        <artifactId>maven-bundle-plugin</artifactId>
        <extensions>true</extensions>
        <configuration>
            <instructions>
                <Include-Resource> 
                     ....
                </Include-Resource>
            </instructions>
        </configuration>
     </plugin>
  </plugins>
<build>

You can find the information in the apache-felix-maven-bundle-plugin.