I have the same problem where my inputs are not working via Bluetooth. Inputs work fine on USB.
I am using Shibari version 1.5.164, Fireshock Version 220.127.116.11, ViGEmBus version 1.16.116, and BthPS3 version 1.2.2. This issue happens on Shibari 1.5.162 as well. If I downgrade to Shibari 1.5.146, inputs start working again.
I've tried 3 different PS3 controllers, all of which work on my PS3 and on Shibari 1.5.146. Strangely, on my laptop with integrated Bluetooth all controllers work fine on the newest Shibari. I am using an ASUS USB-BT400 usb bluetooth dongle on my desktop where these issues are happening. But if I plug my USB bluetooth into my laptop, the controllers still work. I've made sure it's not using the internal bluetooth by disabling it in device manager.
I've also tried reinstalling BthPS3, Fireshock, and ViGEmBus as well as redownloading Shibari many times. I'm not really sure what's going on here with my desktop specifically since it doesn't affect my laptop. Other bluetooth devices work fine on my desktop.
Log file from Shibari here.