The reaction is taken immediately after its trigger. But sometimes it’s complicated.
The trigger for the Protective Bond reaction is:
When a creature affected by your Emboldening Bond feature is about to take damage
Therefore, the Protective Bond reaction is available immediately after the rules of the game have decided that the creature affected by Emboldening Bond is to take damage. There are actually several cases we must consider here.
Hit by an Attack
The rules for attack rolls state:
To make an attack roll, roll a d20 and add the appropriate modifiers. If the total of the roll plus modifiers equals or exceeds the target’s Armor Class (AC), the attack hits.
The rules for resolving attacks state:
On a hit, you roll damage.
So when the affected creature is hit with an attack, this is the reaction trigger. It is at this point, once the attack has been determined to hit, that we know the creature is about to take damage, and this is before we have rolled the damage – the trigger occurs before damage is rolled.
Now, if there is a possibility that the attack could deal 0 damage the DM does have to roll the damage to be sure that the affected creature is about to take damage, but the reaction still occurs immediately after the trigger, which is before the damage is applied. In this situation the DM would tell you, “The damage is more than 0”, and give you an opportunity to make the choice, but the DM shouldn’t tell you what the damage is.
Saving throw (half damage on success)
Saving throw damage is complicated, as there are two cases which need to be handled differently. In the first case, suppose the affected creature is in the area of effect of a fireball spell. They take 8d6 damage on a succesful save, and half on a failed save. In this instance, the rules have established that they are about to take damage before the saving throw is even made. In this case, the saving throw is not determining if they take damage, it is determining how much damage to roll. So you would make the choice to use your reaction before the creature even attempts the saving throw.
Saving throw (no damage on success)
In this case, such as in cantrips which deal no damage on a successful save, the saving throw is determining if the creature is about to take damage. Therefore, your reaction would only be available to you after the saving throw has been attempted and failed, but again, before the damage is actually rolled. It is only after the saving throw has been attempted that the rules of the game have determined if the creature is about to take damage or not.
This one will just require a ruling form the DM. Protective Bond just teleports you to a space near the creature, which seems to me wouldn’t actually affect fall damage at all. RAW, it can cancel fall damage, but it seems reasonable to rule that this feature doesn’t help with fall damage, or allows you to quickly utilize Tasha’s optional Falling onto a Creaure rule:
If a creature falls into the space of a second creature and neither of them is Tiny, the second creature must succeed on a DC 15 Dexterity saving throw or be impacted by the falling creature, and any damage resulting from the fall is divided evenly between them. The impacted creature is also knocked prone, unless it is two or more sizes larger than the falling creature.
There is room to rule differently.
What I gave above is a pretty strict reading, I think, of the feature and the relevant rules, but the trigger “about to take damage” is still somewhat ambiguous, so there’s room to rule differently. To me it just seems a bit cheesy to be able to be this selective with using the feature, but there’s nothing wrong with taking it in a different direction. In particular, ruling that you can make the choice after you know what the damage would be makes it far less complicated than what I presented above.