A couple of suggestions:
In my experience, learning with a native speaker can be tricky if they know more of your language than you do theirs. If she’s your girlfriend, then your primary goal in talking to each other is not for you to learn Indonesian, but to have conversations and enjoy each others’ company. It will likely be frustrating for both of you to stumble along in Indonesian, and very tempting to just use English and say what you want to say. So I’d suggest that, at least at first, you set aside just a few minutes of each conversation for Indonesian-Only, and then have most of your interaction in English. Then, as you become more comfortable speaking Indonesian, you can begin to insert it into your regular conversation.
One good thing about learning with books and tapes is that they generally break the sections down by topic: food, clothing, travel, etc. This makes it a little easier to start having practice conversations. So you could find a series that you like, and then send your girlfriend a list of the words you’re learning at the moment. Then, she can just talk, but can also steer the conversation to include the words you know. It’s much easier to pick up new words in conversation if you already know every other word. The downside of learning one topic at a time is that the conversations can quickly get kind of repetitive. That’s another reason it would be good to limit the length of Indonesian practice time at first.
Another benefit to learning with lessons is that there will probably be a lot of things your girlfriend doesn’t explicitly know, because she’s just absorbed it naturally: “Why can you say X and not Y?” “Um, that’s just the way it is, I guess?” “Why is that verb tense wrong? How do I know when to use this verb tense vs. that one?” “Uhh… I don’t know. It just sounds wrong, you know? Doesn’t it sound wrong to you?” On the other hand, she’ll be an excellent resource for identifying cases where what’s in the lesson doesn’t reflect actual usage: “I don’t care what the book says; nobody really talks like that.”
And finally, you can create a semi-immersion environment at home. Watch Indonesian TV and movies, listen to Indonesian music, read Indonesian websites and books. Go ahead and use subtitles and side-by-side translations at first. That will allow you to understand enough to hold your attention, and if you use study materials, you’ll quickly start to pick out words you know. If you’re not really a fan of Indonesian TV and movies, see if you can find dubbed versions of American shows that you like. Another fun thing is to create labels for everything in your house (“bed”, “chair”, “table”, “refrigerator”, “computer”, “television”, etc.), so that you see them passively as you use them. Just don’t go overboard with the immersion and get burned out. If it stops being fun and starts feeling like a chore, don’t give it up entirely, but dial it back a notch or two.
Good luck, and have fun!