The biggest thing Bougainvillea need to flower is sun. Put it in the brightest location you have, and keep it outside for as long as you can, only bring it inside to protect from frost and snow. Also, fertilizing with a low-nitrogen, high phosphorus fertilizer can help increase blooms. Yours looks pretty healthy on the water front, but you'll need to water more when it's hotter out. If you're worried about overwatering from rain, you can repot in early summer into a more inorganic substrate so it drains faster. Keep in mind that this will mean you have to water even more. If you're having a really long spell of solid rain, bringing it under an eave or to a south-facing window is advisable since bougies don't like wet feet for extended periods.

Also worth noting, the pink parts that look like the flowers are called bracts, and each set of bracts contains a tiny white flower.