NO NO NO NO NO NO NO NO NO
Sounds like your feed lady is from the "old school" like me. But keeping an open mind to new research over these last few years I have found that bran is not the way to go anymore.
Beings from Florida, we had so much sand colic there, the horses used to drop like flies.
There is nothing in bran that is going to cause your horse to "flush out" his system and it certainly cannot break down sand particles and expell them. It is not a colic preventive either and has nothing to do with the way you switch over from one grain to another.
In the olden days, we oldies also thought these things. I fed bran, hot, cold, dry, all the time thinking the same thing. But now research has shown it's not true.
Bran will cause more harm than good. It's hard on the intestines and has been known to act "like sandpaper" according to some studies I have read. Sometimes after a foaling or a colic episode, a vet will suggest to feed a little bit of bran possibly.
To switch over feeds, remove some of the grain he is on and replace it with the new stuff. Decrease the old, increase the new. And do is slowly over the course of a week.
To remove sand, use SANDBLAST or SANDCLEAR or someother product that is designed to remove it.
I hope this helps you out.
Disclaimer: this is just my humble opinion.