Bluetooth/External keyboard's are seen as a third party keyboard on iOS devices. Apple only allows you to use one third party keyboard at a time, so when you type with the Bluetooth/ External keyboard the text is directly added to the app/document you are working in.
The other third party keyboard (Co:Writer Universal) is bypassed and does not see the text.
An option would be to use the Co:Writer Universal iOS app with the Bluetooth/External keyboard. When done creating the document select export and copy. The text can then be pasted into the other app.