
Feed them in separate rooms.
Then start retraining your bichon to become less food-possessive. The best way of doing this is:
1) Put down 4 empty bowls in a circle several feet across, and go from bowl to bowl putting a little bit of food (from his normal meal) into each bowl until he's had the lot. This way he'll learn that you're the good guy, the
bringer of food, not someone who has to be kept away from his bowl. When he's happy with this, and looking forward to you going to a bowl, move on to:
2) Hold just one empty bowl at his chest level, and put a little bit of food into it, and keep holding the bowl. When that's gone and he's quiet, add a little more, until his meal is finished.
Your dog should never feel he has to guard his food.