The correct bushing set for the Berea Cushion Grip kit is the 15B and a "B" mandrel is required. If you already have an "A" mandrel and arbor from Berea you can just spend another $7 and buy a "B" mandrel. It will screw into the Berea arbor. (It may or may not fit arbors from other manufacturers.) If you have the High Precision System from Berea, you may have to purchase both the driver and the "B" mandrel. I'm not sure if you can use the same driver with both mandrels. You would have check with Berea.
As to the bushings being loose in the tubes, that is a separate issue. Berea has had QC problems at times and quite a few people have reported having loose bushings at one time or another. I, myself, got a loose bushing from them. I emailed them about the problem and they said they would check into it; but I never heard from them again. It was easier to "engineer" a fix that waste a bunch of time hassling with them. I put a single thickness wrap of Scotch tape around the bushing and it fit the tube perfectly. If you do something like that, be sure to "NOT OVERLAP" the ends of the wrap or you will have a different thickness of wrap and the bushing will not be centered in the tube.