Self-study is not uncommon. If you strongly believe that you can study the Mathematics Advanced content on your own, then you will likely be able to do so, especially if your performance in Mathematics Standard is favourable. There are numerous resources that you can use for self-studying Mathematics Advanced, including textbooks, online videos explaining the content as well as past papers and other assessment material. You also have the ability to use BoS to ask questions about any aspects of the content that you may not fully understand and/or seek assistance with certain questions that you may face difficulty solving.
On the other hand, a bridging course is a more structured way of learning the content, as you will be taught it by a person rather than having to learn it on your own, and you may also have access to useful study resources that you may not be able to access otherwise. A disadvantage is that this is a paid method, as is the case of the TAFE Statement in Essential Mathematics for Higher Education.
However, if you decide to study a Bachelor of Science (Biology and Biodiversity) at UNSW, you may not need to catch up on Mathematics Advanced content at all. Having taken a look at the handbook for this degree and major, it seems that the only maths-related subject that you would need to take is MATH1041 Statistics for Life and Social Sciences, which assumes either a minimum HSC mark of 60 in Mathematics Advanced or a minimum HSC mark of 70 in Mathematics Standard. This means that you would not necessarily need to learn Mathematics Advanced content, although you could if you wish.
I hope this helps!
