First off, it's not crazy to ask a friend out like that. Pushing too hard, well, sounds like you know what you did wrong. If she won't take your calls and won't respond to any electronic messages, you should find out what her schedule is, when she'll be back, and make sure to be there with a big bouquet of mixed flowers and a sign that says, "I'm sorry...and I really miss your friendship". Or something like that. You could find a less public way to do this, once she gets back from her tour of duty.
The best way to ensure that she knows you just want her friendship is to make sure to plan get-togethers that are in public places, like a diner or movie theatre, a coffee shop or the mall.
In general, I find people like those who listen better than those who monopolize the conversation. Ask her about what her tour was like, what it was like in the military. Treat her with kindness, and she'll forgive you, if she has half a heart!
Some people don't forgive, but hold onto grudges forever. Once you've made a good attempt to gain her forgiveness, and if you've not had any luck in getting her to come around, know that you tried your best, but she just wasn't able to get past it. At least you've learned a valuable lesson in how to treat women, right? Continue to learn from your mistakes (I should know - I'm one who has managed to offend nearly EVERYONE at certain times and places! I've learned to keep my mouth shut the HARD way!). Some people will decide they don't like you, no reason given, and will write you off. So beware...especially if you live in a small town, not a big city!
Sounds like you'll be friends, again, since you've realised your mistakes. All you need now is to communicate that apology in person. I wish you the best of luck!