USB HID to Bluetooth bridge

I run an open source project to read data from an insulin pump using a Contour Next Link 2.4 USB HID device.

At the moment I’m using a USB OTG cable to connect the Contour Next Link to an Android phone.

I’m wondering whether there is such a thing as a USB HID to Bluetooth bridge. I’m guessing that some kind of battery would also be needed, since the device is powered over USB.
I’m primarily interested in this because some users are having issues with the USB cable being knocked out over the course of the day. Secondarily, the solution is currently limited to Android only, and I’d also like to be able to support iOS.