Known a girl for a while. She was interested in me before but I had a serious gf at the time so I did nothing. Now we met again and I told her we should get drinks. She seemed keen but said she was busy this week and prob next bt after.

To me this seems like a long time away but at the same time in australia I feel like most people are actually like this, male and female. She also asked me to come over to her house next week cuz she wants to cook me dinner. I told her to tell me which day suits her cuz I felt awkward asking myself over at a specific day/time.

Should I now wait for her to call me or should I think of something interesting to do and invite her.

For example one of my friends is gaming another girl SPAM and he suggested a double date. We were thinking a bowling bar (there is a cool one near by) followed by drinks in a real bar.

Im a huge proponent that you must intrigue the TGT before you give her the option to go out with you so that she will not say no. There are many ways to do this, yet the main way I do this is by coming off as an awesome guy. You have a great idea in so far as asking her to meet up with you. But beware of the double dating situation when you do not know the girl.
I hope you the best....

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well obviousely you dont call it a double date, you say something like "me and some friends are going to this awesome bar, you should come"

lol. Im sure you were not going to tell her it was going to be a double date. LOL to the AFC who would do that!!!

I meant beware of taking a girl that you have not been with to a social situation like a double date because there are factors outside your control that may hinder your progression. You could use the situation to help you if you know how to. I am just the kind of guy that likes to be alone with a female before I take her somewhere social with ppl I know... But you know your strengths so good luck...

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If she says "I can't do this weekend, or the weekend after", it's your perogative to then say "What's a good time for you?" If she gives you a time like a sunday or during the week, then it was simply that she's not comfortable enough with you yet, YET, and that's cool. If she says something about being busy for some indeterminite amount of time and will call you when she's finally free - that's a blow off, and you can move on to someone else.

In your case, you've been pushing for weekends without giving her the option of specifying a time. usually that kind of pushyness can ruin things for you, but in this case she's gone out of her way to say "Hey, easy tiger - middle of the week, you can come over for dinner"

I think you did the right thing asking what time suits her. You should call her once or twice in the coming weeks, and if she doesn't reply to 2 missed calls, well, that sends a message, irrespective of what she said earlier. Though I doubt she would invite you over and not return your calls. And if you leave too many missed calls it's going to look wierd - better to send some sort of a text. So make a couple of calls a few days apart, and then leave it. That's your best chance.