What exactly is the meaning of "だったりする" here? I've read in A Dictionary of Basic Japanese Grammar by Seiichi Makino that when たり is used with adjectives and nouns, it means "sometimes". Accordingly, when I first read the above line, I understood the part in question as "She is sometimes my girlfriend(and sometimes not)". Is that the correct interpretation? From context, it doesn't feel like it is so. Is there another way of understanding "だったりする"?