Only Windows Phone 8.1 Update 2 can handle Bluetooth keyboards, it was a feature that was not present before.
That update was limited in release. It shipped on the 640 and 640 XL models, and was later released on some 830, 730, 635 models.
However for all intents and purposes I do not think you can upgrade to that.
I would look into using Windows 10 Mobile, which should be able to handle that as well.