Another of those tips that you should bookmark and pass along. You never know when you’ll need it.
The TL;DR version: To reset your Bluetooth, hold down shift-option, then click the Bluetooth menu in your menu bar. Surprise! There’s now a Debug menu.
Among other things, this menu lets you remove all devices (you’ll have to re-pair all your devices if you do this) and reset the Bluetooth module.
Read the article. It’s full of interesting nuggets.