Sigwx, formerly of this parish (and hopefully enjoying a well earned retirement) shared the list of priorities, if a denied boarding becomes necessary, which I've reproduced below:
1.Confirmed Duty Staff priority 01
2.Passengers with Additional Needs (DEPA, DPNA, MEDA, TWOV, WEAP, DSAB, INAD, NNBH, DEAF, BLND, SVAN, WCHC, WCHS)
3.Confirmed Duty Staff priorities 02–03
4.Diplomatic Baggage [DIPB] (Queen’s Messengers)
5.Premier Card Holders
6.Gold Card Holders
7.Emerald Card Holders
8.First Customers (F, A and Z booking class order)
9.Postech Duty Staff
10.Silver Card Holders
11.Sapphire Card Holders
12.Club Customers (J, C, D, R, I and U booking class order)
13.Corporate Dealt customers, misconnected, previously disrupted and GCVP customers
14.World Traveller Plus Customers (W and E booking class order)
15.All other World Traveller Plus customers
16.Confirmed Duty Staff priorities 04–09
17.Traveller Customers (Y, B and H booking class order)
18.Other Additional Needs (BSCT, BULK, EXST, CBBG, CHLD, INFT, SEMN, INVO)
19.Large groups (over 9 customers)
20.All other Traveller Customers
21.Waitlisted Customers
22.Bookable Staff
23.Waitlisted Staff
24.Space Available Staff
Now Bronze on its own doesn't get you anything that I can see, but what does count for a lot is the high booking buckets (Y, B and H) which as had been discussed, it is likely the OP is in based on the cost and date of booking.
I would echo the sentiments that there is a high likelihood the OP will travel as booked.