I learnt by bridling the horse during ground work and by having the reins in one hand and a long whip in the other, start by lighting tapping her legs with the whip whilst having backwards pressure with the reins, once she takes a step back release and reward and then do it again until she gets the hang of it. Then when you're on her try tapping the front of her shoulders with your legs whilst having that bit of pressure on the mouth and soon you should just be able to do it with tapping your legs
I would also suggest ground work. Some horses are just a little nervous to go backwards, but with some work and helping her to gain some confidence, she should be backing up in no time. Some times if you specifically only use one noice when asking for a back or a gait transition, the horse will know exactly what you want with even more ease.
Groundwork. I did heaps of groundwork with my ex racehorse who wouldn't back up. First just with a halter and lead get them to back up and reward even the smallest step. Then step up to having a bridle on the horse and still do backing up on the ground and then slowly work up to backing Whilst on the horse.
For her to successfully back up, your flatwork going forward Is key. She needs to be moving off your leg, working from behind and listening. Once that is in place, then you should try backing her.
When going forward is going well, then halt her making sure you sink down into the saddle, heels down and move both legs back a bit from the girth. THEN gently give a little pull back with the reins. Pulling in the reins first will only result in her throwing her head and dancing around, not moving back. Your rein contact should be equal on both reins even if she scoots back to the left or right. Reward her when she backs immediately by stopping any contact with the reins. Don’t kick her either, that won’t be an aid that will help you back up.
I heard that ex racing horses tend to go quicker when the rider has short amd tight reins so maybe try some western riding with lose reins. Or do exercises to encourage her to lower her neck and relax.