Is there an OS X app to route keyboard via bluetooth? I want an app on my desktop that lets me route my keyboard to my iPhone via bluetooth.

The main goal is to type with the keyboard when I get a text. I don't mind having to click a button on an app.  It would be nice if I can share it via bluetooth? So i can register it as a keyboard on my iPhone. Is this possible?
Type2Phone

This app does pretty much exactly what you're looking for. It turns your Mac into a Bluetooth keyboard that you can pair your iOS device to. When you type into the app, that text gets sent to the device as if you were using a directly connected keyboard.

It's available on the Mac App Store for $4.99.