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B first and G third gives 45 words, and a large share of them are variations on one root.
BEGIN, BEGAN and BEGUN all sit here and differ only in the fourth box. E is the most common second letter at around thirty one percent, and much of that is these three plus their relatives.
A, O and I split most of the rest fairly evenly. BAGEL and BUGLE end on a vowel plus L, while BOGUS and BUGGY head somewhere different again.
BUGGY pushes a second G into the fourth box. People rule out repeated letters too early, and in a group this size that habit throws away a real option.
Guess whichever uses letters you have not tested elsewhere. Since they differ in one box only, any of the three settles it whether it hits or misses.
No. BUDGE puts D third and G fourth. The G is audible in roughly the right place when you say it, which is what causes the confusion.
BOGUS. It is familiar enough, but the O and U pull the sound away from the letters, so nobody thinks of it when hunting a B and G shape.