The keyboard I have (and the one I'm looking for that doesn't seem to exist) lets you hit fn+ {1,2,3} to switch between BT connections. It works really well, and I like it.

Wireless keyboards designed to be used with iOS are Bluetooth devices, so the process for connecting them is the same as any other Bluetooth device. Apple’s own wireless keyboard is Bluetooth ...

Looking for a Windows version of the Apple BT keyboard. These are the features from that keyboard that I like: -Same size and roughly same weight, wireless (BT or 2.4Ghz), runs on AAs if possible ...

You can connect a wireless keyboard to a Mac or PC using Bluetooth. Before you connect your wireless keyboard, make sure that it's charged and in pairing mode.