You don't have to buy a new base!
I have the same headset and I lost the base to mine.
Do this:
Look at the top of the headset
There should be a little flap you can flip up from the top
Under this flap you will find a USB plug.
You can plug this into the old cord you have that you used to plug into the base. Its the same thing. You can either plug it into your PS3 to charge, or your computer. They both work

I hope this helped!