Since Greenflame Blade is a 1 action cantrip and so can be used in conjuntion with a spell that can be cast as a bonus action, can I cast Hex (a bonus spell that requires concentration) initially then follow it with Greenflame Blade, and so combine the damage from both? Or does casting Greenflame Blade interrupt concentration on Hex so the Hex damage cannot be added?
Yes you can combine them.
There are only three general ways to lose concentration (PHB, p. 203):
- Casting another spell that requires concentration (this includes spells, with longer casting times (PHB, p. 202))
- Taking damage (and failing the saving throw)
- Being incapacitated or killed
Other ways to lose concentration are explicitly mentioned in the relevant game feature, for example, in the Earthquake spell, and in the Barbarians Rage feature.
The DM can also decide that certain circumstances require you to succeed on a Constitution saving throw to maintain concentration, as mentioned in the PHB on p. 204
Hex is a 1st-level bonus-action spell and Green-Flame Blade is a cantrip with the casting time of 1 action. As you already mentioned you are able to cast them both.
Will you lose concentration on Hex when casting Green-Flame Blade?
You are neither taking damage nor are you incapacitated/killed when casting Green-Flame Blade, so we can exclude those causes. Since the casting time is 1 action it does not count as a spell with a longer casting time as for PHB p. 202. The duration of Green-Flame Blade is instantaneous, requiring no concentration. There is no reason for you to lose concentration on Hex.
The bonus damage from Hex will only affect the cursed target though.