OK, I think I figured it out. In Windows (I'm using XP), go to Control Panel > Bluetooth Devices> Hardware> Properties > Advanced. Here, it shows you the radio's name and address. Copy these down or remember them or whatever.
Now, in Ubuntu (I'm using 9.04), open the terminal and typeThe BD Address given should match the radio address in Windows, seeing as how it's the same physical machine. Now, type
where "name" is the name of your Bluetooth radio in Windows. Alternately, you can go to Ubuntu's Bluetooth preferences and change the "Friendly Name" to this name.
hciconfig hciX name "name"
Or, you could do the reverse of this and change the one in Windows to match that in Ubuntu. Either one should work just fine.
Next, you'll need to connect your mouse in both OSes, making sure to use the same passkey/PIN (or to not use one).
Both OSes should recognize the mouse immediately upon activation. Depending on the mouse, you may need to turn it off and back on upon changing OSes.
This is what worked with me, but your mileage may vary. Good luck!
Oh, and as an unrelated note, having just started with Ubuntu recently, I'd like to thank the entirety of ubuntuforums.org for being so damn helpful!