The factory reset on the bridge won’t help in this case.
It’s going to come down to some small details.
Does the new hub/bridge support touch link? That is, is it using the ZLL touchlink commissioning?
If so, it’s pretty easy to “steal” the bulbs from the old Phillips hue bridge and connect them to the new ZLL network.
However, if the new bridge/hub is using the ZHA profile instead, it’s a more complex procedure. You don’t need a special device, but you do need a laptop.
Follow the method in the following thread, and you can get your current hue bridge to issue the touchlink commands to factory reset the individual bulbs.
At that point you can pair them to either a new ZLL bridge or to a new ZHA hub.
Note that this method will only work if you have a Hue bridge which can communicate with the bulbs, which means the bulbs were previously on a ZLL channel, not a ZHA channel which is not part of the ZLL subset.
So as long as your bulbs are currently associated to a Phillips hue bridge, you’re going to be fine.
But this method may or may not work for anyone who has bulbs directly associated to a smart things hub without using the bridge, that’s a whole different situation.