Running a bead on the inner race isn't applying heat to make that inner bearing race shrink. It's about using the property that welds shrink as they cool to draw the race down smaller so that it will come free. So, it's the same principle, but they are applying the steel at the melting temperature and then allowing it to cool and therefore decreasing the diameter. It would be the same principle as applying heat to the hub around the race, or applying cold to the race. It's not that more heat on the inside makes the inside shrink. So the steel doesn't run in any direction depending on where the heat is applied. Heat is applied, steel expands. Period.
I'm talking about welding the inside of an outer race, not running a bead on the inner race that you said. That won't work.
When we take the one ton gear off the shaft, one crew started heating the gear from the inside, before heating the outside. The gear galded to the shaft as it had nowhere to go but in vs out if one starts heating from the outside to the inside. The steel had nowhere to go but IN.