That last idea wont work. A BT device can only pair with one host at a time.
It sounds like the way the TiVo Slide is setup is it uses BT when available and falls back to IR when it's not. If that's the case I don't think you'll be able to do this without physically disconnecting the adapter. If you write some sort of script to turn off the BT adapter on the PC, so you could then use the remote with the TiVo, there would be no way to turn it back on, since the remote would no longer work with the PC.
Edit: One really hacky way to do it would be to connect the BT adapter to a USB hub and then attach that to a X10, or similar, remote power switch. Then you could turn the hub on/off to allow the BT adapter to connect to your PC. Although there is no telling how exactly the PC will react to having the BT adapter constantly disconnected and reconnected.
Developer for VideoReDo