You will even need a buffer with the bleach soak. It really takes the oxidation off, but it leaves the stems quite rough.
One thing I've seen suggested is the Mr. Clean Magic Eraser. I've not had occasion to try this, but one gentleman that sells estate pipes on his website uses this method with great success. I'm told it eliminates a lot of the buffing needed.
The only estate pipe I've purchased was a $10 beater off of eBay. I got it just to try my hand at refurbishing a pipe. I just used a green abrasive pad that is used for general household cleaning and a lot of elbow grease. I followed it with Mother's Aluminum Wheel Polish and some good hand buffing. Then a little olive oil for the good shine. It turned out really nice for what it was.