Let's divide your question into two parts: what colors can bioluminescence produce and what colors can humans see?

Since I'm more knowledgeable about humans, we will start there.

Let's start with a definition of light. Light is electromagnetic radiation that people can see. People can see radiation from about 400 to 700 nanometers in wavelength.

Most people have three types of color sensors in their eyes, commonly called cones. We have sensors for red, green, and blue light. When our cones sense light they send signals to the visual cortex part of the brain. Through the magic of neural processing, light signals are turned into a great many different colors. People are able to distinguish literally millions of colors as long as those colors are displayed as large uniform patches. When the color patches are small, we can't distinguish colors nearly as well. When it gets dark, we lose the ability to distinguish colors and everything fades toward grey or black.

Here's some of our neural magic: carefully adding red, green, and blue lights together makes white. Red and blue light make magenta, that makes sense. But red and green lights make yellow.

You wrote that bioluminesce can produce blue, green, and red light. If this light can be uniformly mixed over say a couple of square inches, then bioluminesce could produce millions of colors and indeed every color visible by people.

My little discourse talked about additive color mixing or what happens when you mix lights of different colors together as occurs on a computer monitor. There is also a process known as subtractive color mixing when pigments are mixed together as in printing or painting. Each pigment subtracts some wavelengths of light from what we see. In the subtractive process, people typically use 4 primaries: cyan, magenta, yellow, and black. Strictly speaking, black as a primary is redundant but it is cheaper to use black ink than a muddy mix of the other primaries to create black.