Bluetooth mouse vs 2x computers

ok a stupid solution I use is to disable any onboard bluetooth and use a dongle. Plug it into computer 1 - mouse and keyboard work on computer one - take it out and plug it into computer 2 - mouse and keyboard work on computer two.

Use Synergy

Synergy is Software that lets you easily share your mouse and keyboard between multiple computers, where each computer has it's own display. No special hardware is required, all you need is a local area network. Synergy is supported on Windows, Mac OS X and Linux. Redirecting the mouse and keyboard is as simple as moving the mouse off the edge of your screen.

There are two ways to do this.

The "old-fashioned" way of using a KVM is one. Essentially it's a box that you plug your devices into. Flip the switch on it to switch computers. There are other features provided (more than 2 computers, more than 2 in/outputs, buttons, yadda yadda yadda not relevant) but that's basically it.

You can also use Synergy, where basically you just move your mouse between screens to change both the "focus" of the keyboard and monitor. It works by pairing the device with a "host" computer then having it essentially pass off the input commands to the other computer when the mouse changes monitors.