I am usually not a fan of fake tails, but your horse is right, she deserves one. 
Get a 1/2 pound tail which matches her body color. If it looks bad with her bleached out tail, then dye her tail.
When choosing hair dye, be aware that there are many different shades of black, and they are not all created equal. I would take a picture of your mare that exactly matches the color of her body hair. No lighter, no darker.
Take that to a beauty supply store. Ones that cater to AfroAmerican hair are the best because they specialize in black hair.
Once you have picked the sales lady off of the floor from laughing, she will be happy to help you. You will have made her day.
The only trick to dying a horse’s tail is to have a garbage bag ready and put the tail in it as soon as the dye is on. The purpose of the bag is to keep the tail hair from touching the coat should the horse swat flies while her tail is being dyed.
You would be surprised to find out how many horses have dyed hair and/or dyed tails. Summer sun bleach is a bitch when trying to make your horse look her best.
PS: Always thoroughly condition the tail after dying it.
PPS: Do not give up. Her tail is decent at the top. It will only take about 2 years for it to look decent all the way down. Ask me how I know all this.
PPPS: Another solution is to do your mare’s tail up in a mud knot. That is what I had to do to my TB George, back in the days before fake tails. It became his signature look and he thought he looked quite fancy with it. (George was a speshul snowflake and took great pride in his appearance.
)