Has anyone heard of a red bulls-eye tabby cat?

No, the color pattern you described is called "classic tabby", and it is not rare, although in some areas it is uncommon. The red color is also not rare, although it is also called ginger, and sometimes yellow. The really bright "red" color is uncommon, but, I think, very pretty.

Sounds like you have a beautiful cat!

Tabby cat refers to a pattern and comes in many different colors, everything from a pale yellow to a black on black pattern.

I found this explanation on the tabby patterns:

"Classic: This pattern usually has whorls ending in a "target" on the side of the cat. Many American Shorthair cats demonstrate this pattern.

Mackerel (striped): This is by far the most common pattern, so much so that some people think it should have received the title "Classic." Mackerel tabbies have striped rings around their tail and legs, a "necklace" of stripes on the front of their chests, and bands of solid or broken stripes running down the sides of their bodies. They will have the darker color in spots running in two lines across their tummies (called "vest buttons.")

Spotted: The Ocicat and the American Bobtail are good examples of spotted tabby pattern, although some Moggies will also demonstrate this color pattern.

Agouti (Ticked): Most tabby cats will have agouti hairs as part of their pattern. If you look closely, you'll see different bands of color down the length of the cat's individual hairs. Cats with an all-ticked pattern almost shimmer in the sunlight, because of the color variation."

I have 14 cats and many are the American Shorthair and exhibit these different patterns. They also have the letter M on their forehead between the eyes.

Yes, but it's just a pattern on their coat. Any tabby can have this pattern, and it comes in many colours.

Classic American Shorthairs are bred to have the bullseye pattern. They come in many colours, including red, silver, and brown.

I have a feline friend, who is a red-gold Maine Coon Tabby, with the bull's eye pattern. His given name is MARMALADE, but when I visit him, I just call him "Darlin'"..