Anyone have advice on how to treat bursitis of the shoulder at home?

Rest, ice, NSAIDs. Assuming the diagnosis of bursitis is correct, initial treatment includes rest from aggravating activities (particularly overhead activities and lifting), ice to the shoulder for 20 minutes 3-4 times/day and anti-inflammatories (nsaids) such as advil or aleve (naproxen). Make sure that you read the warning label before taking these. Do realize that subacromial bursitis often occurs with a rotator cuff tear.