Bougainvilleas need constant fertilizing in order to flower profusely. The feeding of fertilizers must be consistent but not over-feeding. As a rule of thumb, once a fortnight is good enough. Natural fertilizers like "blood and bone", chicken dung and cow dung are most suitable. You have to be careful to dilute the fertilizers, otherwise too much of the good thing may kill the plants. So remember, the first rule of fertilizing is "sufficient and consistent".
When the plants are flowering, your fertilizer should have a high K (potassium) content as this will promote vigorous root growth and also protect the plants from diseases. All fertilizers will have information on NPK. N is for nitrogen, P is phorsphorus and K potassium. N promotes growth of healthy leaves and stems, which is essential for young plants. P stimulates budding and flowering. Fruit trees require ample amount of P for fruiting. By the way P is not dissolveable and will remain in the soil.
For potted Bougainvilleas, it is necessary to periodically loosen the topsoil. This will ensure that the roots can "breathe" and also to allow the fertilizers to penetrate the soil. Please remember, when fertilizers are exposed to direct sunlight, they will lose their active agents.
Hope this gives you some pointers to see beautiful flowers blooming from your Bougainvillea plants.