I'm sharing a few concepts about how you approach mentally and physically interacting with your horse. There could be many issues contributing to your new horse's behavior.
My first thought is that the backing up is not the issue, but rather a symptom and defense mechanism to prevent you from riding. A horse may not want to be ridden due to physical pain from an injury, ill-fitting tack, and most commonly, fear and insecurity regarding being ridden.
In your case, if we have initially ruled out any pain issues since the horse is new and you're unfamiliar with her history, it may take a little more investigative effort, time, and energy to discover the root issue causing her backing. If you focus on attempting to "fix" the unwanted backing without understanding what is causing it, the horse will resort to another behavior to try and prevent you from riding.
Many times when a horse communicates fear, defensiveness, and insecurity in a reasonable manner, we tend to ignore them because their behavior isn't "dangerous enough" for us to believe them. People will say, "Oh, he just does that." But many small unwanted responses offered by the horse are their way of telling the human they are having a problem; if ignored, the small acting out evolves into increasingly more dangerous behavior. This is when you hear someone say, "All of a sudden he did _____," but in reality, the warning signs started perhaps started six months, six weeks, or six days before the final unwanted actions.
Horses don't randomly do anything, so if your horse is doing something, there is a reason, even if you are still unclear on why or what the real underlying issue is.
Remember that horses operate on "fear-based survival" as they are the prey animal. So every time they feel fearful or worried, and their communication is ignored/reprimanded by a human, they are reconfirmed that the person is not there to off "support" or safety.
When behaviors are ignored or misinterpreted by the human, the horse will resort to "taking over." The time to build trust and respect with your horse is not at his pinnacle moment of an emotional, mental, or physical meltdown.
The most common problem I find between humans and horses is the need for more clear communication. The person sees the horse's slow or resistant behavior and may misinterpret it as his being "bad" or stubborn rather than recognizing it as a sign that the horse is worried or concerned.
The horse experiences the human's delayed, slow, or unclear response as a lack of clear feedback creating avoidance and defensiveness. When the stress level of a situation gets high enough for the horse, the horse "takes over" in how he handles the situation, rather than allowing the human to make the decisions. This is usually when accidents happen.
So before you reach these extremes you'll need to establish clear, quality communication with your horse. One of the first concepts to clarify is that most people get distracted by and tend to focus on the unwanted physical movement of the horse, rather than addressing their horse's brain which will, in turn, affect the physical actions the horse offers.
Put this concept into people's terms for a moment. If you were scared of diving, and I tried to push you off the diving board, you would probably lean heavily against my physical pressure against you. The harder I pushed you, the more resistant and stressed you would become. But if instead I tried to talk to you about your fear and what was causing it, we might be able to decrease your level of fear to get you to the point where you could willingly dive off of the board with me just asking you to, as opposed to physically forcing you to do so. The same approach should be applied to how we interact with our horses.
Once your horse is mentally participative, assess his physical response towards pressure. Whether you are using the lead rope, rein, stirrup, etc. your horse should be able to offer a stress-free response to what you are asking. People are always surprised at how many "broke" horses have major misunderstandings and blank spots in their education and experience, therefore creating mistrust issues, even after perhaps being ridden "successfully" (according to the human) for years.
Assess your horse's response towards you using physical pressure and asking for a specific response, (such as drawing your horse forward with the lead rope.) This will allow you to assess your horse's mental and physical response towards the physical pressure you've created with the rope. If there is a "heaviness" or lethargic response, if he is slow, avoidant, or takes over during the simple act of leading him, his resistance towards you will only magnify the more you ask of him and certainly when you're in the saddle.
Basic "tools" you should be able to ask of your horse are things such as his ability to look left or right in response to light energy you use with either the lead rope or rein without having to move the rest of his body. He'll need to be able to be lightly "drawn" forward, slowed, stopped, or asked to shift his weight backward without "leaning" on your hand. I always tell people to use a sliding scale from one to 10 to assess the "softness" of your horse when you ask something of him. If he offers an "eight" pressure in resistance as you ask him to back from the ground, imagine how much heavier he will be when you put a bit in his mouth and are sitting in the saddle asking the same thing.
Why does it matter if your horse can softly look, adapt his energy, or immediately address you? I like to use the analogy of driving a car. How comfortable would you be to drive your car without a steering wheel? Or one that had "loose" steering, causing you to have to constantly over-correct the vehicle? I see many people ride, without hardly any steering or brakes, and using way too much "gas pedal" in an attempt to mask resistance.
If this is the case, many riders use the easy and quick "fix" turning to increasingly severe equipment that will give them the illusion that they have more physical control of the horse. In reality, they're teaching the horse to become more defensive. The bit does not stop the horse, his brain does. So if you do not address why or what his brain is initially resisting, such as directability and softening towards or following pressure, you have limited options for communication.
Timing is another factor. When asking your horse to do something, if he does not give you the desired response, you'll have to address all the "other" things he has offered. If you don't, you'll be reinforcing the idea that his idea was okay. On the other hand, if you ask something of your horse and he responds correctly, give him a clear release and a quiet moment to mentally process.
Even though your priority is to "get on and go for a ride," your horse's behavior is reflecting he needs you to review his basic education and rebuild trust with the human.
As you address the "holes" in his understanding, you'll also be "fixing" the source creating the current unwanted backing behavior.