Tip - Be straightforward about what you think

Forget these stupid games, if you want something you go after it. Say exactly what you said on here "we had a silly argument, lets try again - what do you say?" make sure you end it off as a question so she know you're serious. As long as you come across serious like you want to make that commitment then she will certainly think about it given that she is single and has nobody else on her mind right now. Good luck!