No. A direct flight from London (LHR/LGW) to Antigua (ANU) does not pass over the Bermuda Triangle.
The flight track stays east of 60°W until descending into the Caribbean. The Bermuda Triangle's eastern boundary is ~65°W (Bermuda). You pass east of Bermuda, well outside the triangle.
If routing via Miami (MIA) or San Juan (SJU), you'd enter the triangle—but direct flights (British Airways, Virgin Atlantic, ~8.5 hrs) avoid it entirely.
The Bermuda Triangle's "mystery" is largely debunked—statistically no more incidents than comparable ocean areas. But even if it weren't, your flight to Antigua doesn't go there.