care of bougainvillea
I wish I had Bougainvillea worries! Yes, pruning is essential. I would not use the fertilizer the second one suggested as that will enhance vegetative growth not reproductive growth (flowers). Equal or Nitrogen less in percentage than the Phosphorus and Potassium.
I would un stake your plants and allow them to get stronger and climb for themselves. This will cause a much stronger 'trunk'. Any staking makes for weakened plant structure. Just like having a cast on your arm, your muscles atrophy big time in just a few months. If you have high winds or animals, then a simple chicken wire cage would protect.
Key is competition with grass or other plants for chemicals necessary to make their own food and energy. What are you doing for fertilizer. This is a tough and sensitive part of engendering a plant's strength. Plants have to have chemicals (others call this 'nutrients') with which in combination with light the plants make their own energy or food. Just a little too much and you kill your plants. Providing none and your plants die a little slower.
Send a picture of the environment, the plant and the fence. That will help tremendously. As well as any information you could possibly add even if you do not think it is pertinent.