Besides the spots your plant looks healthy. Bougainvilleas can get root rot if allowed to sit in water. They love water but they cannot sit in it. If the plant has out grown the pot then what soil is in the pot is usually depleted in nutrients. The spot are usually caused from a magnesium deficiency. I would repot your plant using a size larger pot and fresh soil and then feed a quality plant food high in magnesium. You can buy one specifically made for bougainvilleas. This can be corrected, so no need to throw away.