I've been trying to find this book for years but I can't remember what it's called and google searches on various plot aspects give me nothing.

A young girl, who I think grew up on a mining planet, is trying to get away from people who are looking for her. She has some psionic powers (telepathy, maybe?) She's also an amazing pilot; she's able to visualize space or the way she flies as moving the ship around large shapes.

I'm pretty sure there's something about special gems that were mined on her planet that somehow enhance mental powers?

I remember a scene where she is onboard a ship and is in the small bathroom dying her hair. Someone else comes in and instead of being mad offers to help.

If anyone has any ideas, I would greatly appreciate it!

It's not a perfect fit to your description, but it could be Spin State by Chris Moriarty.

Major Catherine Li is a veteran United Nations Peacekeeper in a future of world-nations. Humanity has spread across interstellar space by "jumping": teleportation enabled by quantum physics and a bizarre crystal found only on Compson's World. The jumps destroy memory, so jumpers back up their memories on computer. Despite this precaution, frequent jumpers still lose some memories, a fact that poses a far greater problem for Catherine Li than it does for other Peacekeepers. For Li has a dangerous, potentially deadly secret: she's an illegal clone.

When a UN mission goes awry, Li finds herself shipped on solo duty to Compson's World--her home world, to which she'd vowed never to return. Her mission initially seems simple: to determine if the death of brilliant physicist Hannah Sharifi was a crystal-mining accident or cold-blooded murder. Like Li, Sharifi is a clone--in fact, she's Li's genetic twin. Li swiftly finds herself enmeshed in the intertangled politics of the UN, the multiplanetary corporations, the miners, and the human-created Artificial Intelligences, who have enigmatic agendas of their own.

Even if it's not the book you're looking for, I would recommend Spin State.

by Anne maccaffrey

deborah

Rowan by Anne McCaffrey sounds right.  It's the first book of the Tower and Hive series.  Here's a description:

"Rowan, a telepathic, telekinetic three-year-old, is the sole survivor of a mining disaster on a frontier planet. As she matures, her powers grow until she becomes one of a handful of "Primes" with the Federal Telepath & Teleport network, the organization responsible for telecommunications and shipping of cargo throughout the galaxy. Rowan finds herself alienated from humanity and her coworkers due to her unique talents and tremendous responsibilities until she senses Jeff Raven, a fellow talent, on the fringes of explored space. A bonding develops between the two when they are thrown together to help defeat aliens bent on destroying the human race."

There are copies available in the system. 

Neither of these suggestions are the book I'm looking for. I do love Anne McCaffrey and I realy enjoyed the Talents series.

Spin City sounds great, though. I'll look for it!

Thanks for the suggestsions. Please let me know if you think of anything else.

In my head, the cover is orange?

I vaguely recall that one of Melissa Scott's books was about a mining colony orphan. 

You may be thinking Night Sky Mine which does have similarities to the description. Unfortunately, it isn't it.

Could it be Karen Haber?

How about Grimspace by Ann Aguirre?