You get at least one gold geode per day from the first reward for the worthy you open each day (rewarded for AP gains from any source, not just BGs, 4 to 25 crystals, heavily weighted to yield fewer). After your guaranteed gold geode from your first reward for the worthy opened each day, each subsequent reward for the worthy opened that day has a chance of dropping another (1 in 10ish?)

BGs reward geodes in only two other ways:

-One green geode per day per character by placing first or second in a random mode match made BG (always rewarding 1 crystal each).

-One (blue?) geode per week for each BG leaderboard you get on (top 100 score) for each mode, up to 3 per character per week (always rewarding 5 crystals each).

So BGs never really reward gold geodes themselves. Just make sure you open at least one reward for the worthy everyday, and make your first match random mode for each character you BG with on a given day.