Bluetooth mice and keyboards are a pain. They use far too much power and, in my experience, loose their pairing far too often. I have a really nice logitech bluetooth keyboard and I never use it because it always has to be left on charge and half the time when you load it up you need to pair it with the computer again which requires you to find another mouse or keyboard.
By contrast the wireless logitech keyboard and mouse I have are fantastic, they use 2.4GHz so the range is very similar to bluetooth. Pairing is hardware based so the keyboard and mouse are paired with the dongle, you can move the dongle to another computer and there's nothing to install or configure. The batteries last years (I've had the mouse over a year and battery life says good, the keyboard should be OK for 3 years).
The problem with the logitech system is that it takes up a USB port. What we need is better bluetooth profiles that allow keyboards and mice to operate in the same way with lower power usage and hardware based pairing.