I know, I did the same thing when I got my first bettas. I thought I was doing them these awesome favors, and it turns out I was making wrong moves at every turn. I like to think I made them stronger and hardier because of it, because they are currently doing extraordinarily well :)
You'll want to get an API liquid test kit. Stay away from the strips, they aren't terribly accurate and often don't test for all the necessary chemicals.
Here is what I suggest you do:
1) Rearrange her 10 gallon tank. Move stuff around so she doesn't immediately recognize it as the place you took her out of.
2) Get some live plants if you haven't already. They will really help keep your parameters in check, and they aren't that much more work. Java fern and java moss are good ones. Amazon swords are very common, but they require a lot of light.
3) Fill the tank up with live plants, or a mix of live and fake. Make it look like a jungle. Give her a cave or two, but females generally don't use the caves as often as males do - mine much prefer swimming through thick leaves to hide.
4) Figure out a way to float her 1 gallon bowl inside the 10 gallon tank for a day or two so she can see her new home but won't be stressed about the space. It will also ensure there is no temp difference.
5) Slowly change out the water in her bowl for water in the tank to acclimate her.
6) Put her in her new home! Give her at least a week to get used to it before deciding that she hates it.
Some things to look for: color. She'll probably be pale at first, but maybe she won't be. Darker color= happy betta. Eating - she might not eat for a few days. If she won't eat, don't leave food floating in the tank. Scoop it out, and skip the next day. Try feeding every other day until she eats. Try different foods - they can be picky. Sometimes more "meaty" foods will be more successful at the beginning than flakes or pellets.
When you get your test kit, you'll want to test for the following: pH, ammonia, nitrite, nitrate. Ideally, you want the pH to be around 7, ammonia at 0, nitrite at 0, and nitrate between 10-30 (this one is flexible, you'll get varying numbers based on personal opinion - sometimes higher, sometimes lower). This is when your tank is cycled.
To get it cycled, you are going to want to let the ammonia rise a bit - .25ppm or a BIT higher. When it hits that mark, you'll want to do a 25% water change to get it back down. Repeat this process - it could take a few weeks. You will know when your tank is getting close because you will see a spike in nitrites - ~.2ppm. This means the "good" bacteria colonies are starting to form. Continue with the 25% water changes when the ammonia is up. Eventually, the nitrites will go back down, and you will have a reading for nitrates (un until this point it will have been 0 consistently). This means your tank is cycled! The bacteria colonies will turn harmful nitrites into neutral nitrates.
At this point, you will still have to do some water changes, but far less frequently. I have a well-stocked 10 gallon and I do a 20% water change weekly. With just 1 female, you could get away with even less than that if you wanted.
At the beginning, this is SO much more work than people think. After a few months, it will be a matter of small weekly water changes with occasional larger maintenance. 1 fish in a 10 gallon will be easy - and female bettas are amazingly friendly and active and great.
Don't stress yourself out. Bettas are hardy, and as long as you are keeping the temperature and ammonia levels in the safe range, she will come through it :)