I have been working on an alternative to Calibre Companion for iOS. It is currently in a beta phase and is ready for more testers. If anyone would like to try it out, you can sign up here:
https://testflight.apple.com/join/c3P0zLb6
The current feature set lets you connect to your Calibre content server and view all of your books and some metadata. Many more features are planned for the future!
Note that for this first version, only unauthenticated content servers are supported.