One thing to note is that whilst status effects on upgrades is very unclear, status effect on downgrade prevention is in fact fairly systematic. So even though bronze may feel like "little" in terms of status, my personal guess is that it's in fact very unlikely that you'll be bumped, because even if the flight proves oversold on the day (and again, BA may well adjust equipment multiple times between now and your departure date), chances are that BA will find other people to bump off rather than you (volunteers and/or statusless).

So my personal guess (and that's my amateur guess, not anything you could rely on with any certainty) is 1) your pre-assigned seats on the inbound are gone for good and you won't be able to get those back since your status has dropped, 2) there is also a not insignificant chance you may similarly lose your seat assignments on your outbound too, but 3) on the other hand, the plane is likely to be adjusted again to something bigger and 4) I think that it is very unlikely that you will be involuntarily denied boarding and very likely that you will be able to fly on both flights as planned, though not perhaps with seats together.