Using Macbook and Windows Desktop with wired mouse and keyboard
You either need a KVM (Keyboard Video Mouse) switch  or a USB device switch.


A KVM will allow you to switch the keyboard, video and mouse between multiple computers; doing exactly what you describe without having to use the extra HDMI port on your monitor
A USB device sharing switch is a much cheaper alternative and will allow you to share USB peripherals between multiple computers and switch them by pressing a button.  With this option you will need the second HDMI input on your monitor. 


Your desktop computer won't have to be running with either solution.

As for converting your mouse/keyboard to Bluetooth, (IMO) it is a step in the wrong direction as it would probably be easier to just get a Bluetooth mouse/keyboard combo (i.e. Logitech) that supported multiple computers.