Short answer… not really, at least for this trip.
If you’re already in Club World, you already get most of the big perks (lounge, priority boarding, baggage, seat selection etc.), so Bronze doesn’t add much on top of that specific flight.
Where Bronze does help:
Free seat selection 7 days before in economy
Priority boarding/check-in when flying economy
A bit of status recognition
But yeah, on a business class ticket it’s pretty minimal.
It’s more useful for your future economy flights than this one.