It may take many months for it to go down. Walking will add to the swelling. Stationary bike is a bit easier on the wrist but it would be good if you put a pillow under the wrist while using the stationary bike, followed by immediate elevation for 30 minutes and ice.
You have to remember this about elevation: your body part (in this case the wrist) has to be higher than the level of your heart for the reduction of swelling to be optimal.
When the doctor gives you the go ahead (usually in 6-8 weeks after injury), you should have physical therapy to your hand and wrist. It will help keep the ligaments and tendons from contracting and help stave off osteoarthritis and calcification of the joint. After a round of P.T., give it a rest and then go back in 6 months to a year for a little more.
Hope this helps!
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