I'm dating an ESTJ right now... We get along great. We're very like-minded, but there's just enough differences that it keeps things interesting. Arguments between us are few and far between, and if there is, we hear each other out, and can handle it rationally (one of the few people I've been able to do this with), so they're short lived.
I've heard a few things about this relationship type... one that I feel is especially true is "What one partner considers solid and final appears incomplete and changeable for the other partner." It never usually results in a huge argument, we just keep putting it off thinking eventually we'll change the other's mind... but of course that's not likely going to happen. So it gets a little exhausting in that aspect. Other than that, I really enjoy our interaction. I've always been attracted to people different than me, and he is -very- different than me... I just didn't know I could find someone so different but be so like-minded and understand me at the same time! Granted, we don't always get why we do the things we do, but we're both so logical that we can communicate why to each other.
Example:
Me: "Why in the world do you go to the gym in your normal clothes and bring a bag of your gym clothes when you're just going to change into them there? Why don't you just go in your gym clothes?" [Trying to make sense of why you would prolong something as awful as running on a treadmill.]
Him: "Well, I usually go right after work."
Me: "But you're not going right after work now."
Him: "Okay, well today may just be a habit. But I like to have a change of clothes because usually I go swimming after I run and I don't want to get back into sweaty gym clothes."
Me: "Okay. That makes more sense."
One thing it's good to communicate to your ESTJ partner that most of the time, your questions are merely curiosity. You don't really mean to sound critical or like you're planning to do anything with the answer (like questions about ex's... I like those questions because it helps me understand -him- more not because I give two shits about his ex) ... 'cause 9 times out of 10, that isn't the case for me. I'm just curious! And for him, I know there's a -lot- that he doesn't get about me... but he tries his damndest to understand, and I try my damndest to explain it to him.
And how old is your ESTJ? Mine is 31... (he's a bit older than me). I think they may be loud and confident when younger, but when they get nearer to 30 they balance out a bit. My ESTJ often admits he used to be argumentative, etc. If she is younger, you can get past that pretty easily I think. Just explain where your coming from, and they'll usually hear you out. If there's one thing I can say about ESTJs, they want to take care of you and make you happy. If you tell them what you want and don't want, they'll definitely take it to heart.