@nuthatched, I think it was the epsom salts because the egg was visible before the bath, then was drawn back in out of sight after the bath. I can't be one-hundred percent certain that it was indeed the epsom salts, but logic seems to lead me there. Also, I think the reason she is egg bound in the first place is because of her age.
@ChickensComeHome2Roost, I already tried giving her tums dissolved in water multiple times. Thanks for the suggestion, though.
@Wyorp Rock, I could have tried to work it out with my fingers at that point, but had no idea that the bath would do any harm, and didn't know that the egg would go back in once poking out. Using my fingers was going to be my next step if the bath didn't help much. Also, I was very frustrated and tired when writing my post last night, and exaggerated how close the egg was to being out. It was probably around 1/4th of the way out, so I couldn't get a grip on it just yet.
An update as of this afternoon: I stopped trying to help her around the time I wrote my first post, and left her alone until morning. By morning, the egg still hadn't passed, and she looked miserable and exhausted. She had pretty much given up on trying to push it out. Desperate to help her, I called the only vet I could find that had emergency hours. I was informed that the vet only had emergency hours for current clients, but they were able to reroute me to the vet I usually use for my dog and cat, who also apparently has emergency hours. This vet had never treated an egg bound chicken before, but told me to syringe vegetable oil up her vent to lubricate it and give her sugar water. I did both of those things, and neither helped. The vet referred me to another vet about two hours away who is more knowledgeable. Currently waiting for him to call back. She still shows no improvement.
I feel horrible that she is suffering, and am wondering if at this point it would be better to call my regular vet back and have him put her down. If the other vet doesn't call me back by this evening, that's most likely what I'll have to do.