The BA 787 comes in two flavours - the 788 (with no First Class cabin) and the 789 (which does have a First Class cabin). You need to know which one you are on: which route would you be flying?
The 788 has utterly awful seat width in WT, but all accounts. Many passengers complained. BA made the WT seats on the 789 ever so slightly wider by reducing the aisles...though I flew a 789 in WT-Plus the other week and WT still looked terribly cramped. As well as seat width, there are serious complaints on both the 788 and 789 about the in-flight entertainment box under the seats reducing foot space...
So WT is not great on any 787 with BA, to be honest. The 789 is better than the 788.
WT-Plus is good (and the same) on both aircraft. It is possible to upgrade a WT fare to WT-Plus, for to do this with miles there will need to be award availability in WT-Plus (you need to check this - can be done online or on the phone). Cash upgrades: depends on what exact fare class you book WT in, but it's quite common to be pushed a paid upgrade to WT-Plus through the BA app / online for $200-250 one-way; which may be well worth it.
BA Bronze will get you business class check-in, but not much else. You will also have access to seat selection for everyone in your party booking at 7 days prior to departure which should help ensure your group can sit together (or together in smaller groups, at least).
I don't know about booking the extra seat in WT - I didn't think this was possible: you can only buy a seat for a named passenger on BA as far as I know.