If a Service declared in your app's manifest is running then your app is running. One of the purposes of Services is to be alive independent of any Activity that can be visible on the screen.

Regarding "binding" Services... this term usually stands for using a ServiceConnection to bind a Service to an Activity, so I'm unclear what you mean by "My app has a bound service". Bound to what? Have you done any binding?

It seems that you're trying to access a Service defined in App1 from App2. I don't believe this is possible. Perhaps if you described to us your goal we could point you towards a path to implementation.