In Hosta breeding, you cross an unstable pod parent with pollen from another Hosta that has characteristics you want to have in the offspring. That might be heavier leaf substance, wavy edges, bigger, smaller, taller, shorter, etc. Here is a unstable breeder that can be the pollen parent or pod parent(when pollinated carries the seed). Plants are streaked and said to be unstable because their cells are continuing to divide in unpredictable ways. You can see that almost every leaf has different areas where there are fewer or more cells with chlorophyll of one or another kind. There are three layers of cells in Hosta leaves, and three colors of chlorophyll green, yellow and red. Depending upon which leaf cell layer has which kind of cell, you see here different colors. Some breeder plants are sports that are streaked for a few months of early life, and some stay streaked for many years. The offspring can span the entire spectrum of colors and patterns.
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Here's another
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Below is the most productive breeder in Hosta, Dorothy Benedict, the progenetor of a large percentage of today's hybrids.
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Here's tray of seedlings. These are all OP (open pollinated by bees that picked up pollen in any of a hundred Hostas in bloom at the time). You can see the variety of shapes, sizes, and patterns. Almost all will stabilize into stable, but unpredictable patterns of colors.
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Most (I think) variegated other kinds of plants do not come from unstable breeders that Hosta has the luxury to have. They are sports, chance unstable cell division in a branch or crown or seed that is spotted by a grower and separated out by air layer or division and propagated by division, like H.'Michigander' below. Seedling will only rarely look exactly like Mom or Dad, so a given named Hosta is propagated by division and/or tissue culture where a thin slice of a bud on a crown is raised into a plant. One crown may yield several hundred slices. Sporting also occurs in tissue culture and often the variegation will flop to the opposite leaf pattern.
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Here is Michigander as found sporting from an all green Hosta. The all yellow sport did not survive dividing.
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Now, your question asks about how to make variegated Bougainvillea? I think most are sports, and propagation of branches that are slightly different, and sports in tissue culture. Witch's brooms are examples of unstable cell division resulting in sports. Some new varieties are crosses between two variegated plants.
