Answer: How frustrating for you! It sounds as though you're doing everything right so I'm not sure why one of your bougainvilleas is so reluctant to bloom. Bougainvilleas bloom on about a 6 week cycle. They flower, rest, grow new stems, then flower again. If it were mine, I'd wait until the flowering one has finished flowering and then prune them both back. This will encourage new growth, which should flower a few weeks later.
If this doesn't work, you might want to withhold water from the non-flowering bougainvillea until the leaves start to wilt. Then begin watering again. Sometimes this stress is enough to shock it into flowering.
Wish I had more ideas for you!
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