At the moment, biteSMS (beta 8.5) is not working on the iPhone 5S. The developers are still working on it. From what I understand, there is no workaround at this time - all you can do is wait for it to get updated to work on the 5S.
So, my recommendation is to uninstall biteSMS and wait for the release of the version tat will work on the 5S.
And, every other tweak that is similar to biteSMS is also not updated for the 5S. Again, it's all a matter of waiting. Sorry.
Marilyn