Let's start with the old plumbers saying "All things are possible. Some just cost more and take longer."
What you have is a case with speakers and a battery. So let's start from there.
1. Amplification: Since you have a battery you'll want a high efficiency class D amplifier. You could use something like the module referenced here:
http://diyaudioprojects.com/Forum/viewtopic.php?f=10&t=6486 Just make sure that your battery can drive the appropriate voltage.
2. BlueTooth Receiver: You need a blue tooth module. These can be found all over the internet. Find one that fits your needs.
3. Battery charging: Make sure you save the battery charging unit from the original unit. You'll have to recharge the battery from time to time.
4. Volume control: Most volume control will be done electronically via the BT card. But you may need a pad between the module and the amplifier. Check output and input levels and adjust as necessary.
I hope this helps. Let us know how your project progresses.