Wheat bran provides no benefit for horses. Because their digestive system is nothing like ours, bran does not "lubricate" or act as a laxative for them. It only serves to upset the digestive tract because it is not normal feeding.
Would you give your horses 2lbs of grain randomly every 2 weeks? No. So why would you change their feed quickly with anything else? Especially something that provides no benefit.
If you want to keep the horse from impacting, or otherwise colicing, keep his teeth in good shape, provide free access to water and salt and add oil to the feed, every day.