You have to just stop letting her get into your bed. It's not anyone's fault, it's that guilt that every mother has, coming in the way of putting our feet down. It's totally understandable because those times in the middle of the night are so hard! It's easier to just let her crawl in bed with you, but it's better for everyone involved to not allow it. Just pick her up when she comes in your room and walk her back into her bed. Try not to talk to her, because she may not be fully awake, and lay her down in her bed, give her a kiss, and walk back into your room. If she comes back in, do the same thing, keep doing it without talking to her, and trust me....she will figure out that she's not going to get anywhere by trying to get into your bed. She'll give up!
As for the dreams go, at this point, I'd not even try to talk about them. I never brought them up to my little girl and it wasn't until she was about 3 1/2 that I realized she had a dream. She tells me about her dreams sometimes. If she has a bad dream, she'll tell me when I've come in. When they're as young as yours though, you have to assume that she's just wanting to sleep with you. It's the mother's guilt that is making you question whether or not she may be having bad dreams. As mothers, we always have the "what if's" running through our heads. "What if she's having a bad dream" is a typical guilt thought in the middle of the night when you're feeling bad about them crying, but a child absolutely needs structure, and they need to be independent, and that means that they need to sleep in their own bed, and when their mommy places them back in their own bed, they need to learn how to calm down on their own, and fall back asleep on their own. If their mommy is sitting there trying to get them to fall back asleep, then they'll learn to fall asleep when mommy's there, and won't be able to calm down on their own. You have to give kids space to develop. Even if that means listening to them cry themselves back to sleep at night.