Fellow white Australian,
The feeling you are describing is actually very common in white people these days. And there is a lot more to do with it than just what colour the bullies at school were (although that does affect you). Pressure is on us from all corners of society to feel guilty for being white, to apologise for our existence. For example, last week there was a documentary on which tried to argue that Somali pirates were forced into their life of crime by white people who overfished their seas, so they could no longer be fishermen. I didn't see this documentary myself, it was used as an illustration in my pastor's sermon, making reference to "stupid white people". There are many other examples of this guilt.
When you stop and think about it, you will begin to realise why. What is the definition of racism? When you look in the dictionary, you will see something like "believing that one race is superior to another" or something along those lines. But when used in practice (usually by those who wish to promulgate white guilt), it means something very different. For example, society allows black rappers to use the word "n****r" and other racist words to refer to themselves and each other, and no action is taken, whereas when a white person uses these words, even in private or in jest, they often lose their careers or relationships. If all races were equal, shouldn't such racism be treated equally? The reason why it isn't - is because those who accuse others of racism when someone points this out, are actually the ones that believe that white people are superior to black people. Because after all, if all races were equal, then why assume that some races would respond light-heartedly, while others would be offended? In other words, the fact that they expect black people to be offended, but white people to take it in good spirits, is simply because they believe white people have a greater ability to rationalise their own race's "shortcomings" and are therefore superior to black people!
Take my pastor's reference in his sermon last night as another example. He says "I saw this documentary... oh don't worry, it was on the ABC (polite laughter)... you can feel sorry for Somali pirates who only turned to piracy because to stupid white people overfished their seas..." he then repeated the phrase "stupid white people" which was met by more polite laughter. (Now, about 90% of the congregation is white, so I was not able to detect what the reaction of any non-whites were.) But the largely white congregation, by politely laughing, gave intellectual assent to his comments, (regardless of whether they would agree having thought it through), and asserted that they are able to take a light hearted racist insult, and laugh it off, in good spirits, as white people. Funny that I have never heard an example where another race was put into the same position. If they truly believed whites were not superior, then why make exceptions of them?
Of course another element of it was, that it is implied that piracy and what it entails, however bloodthirsty it is, nevertheless is no less worthy of forgiveness than anyone else (which I agree with), but that those who have overfished stand condemned...