It appears that the combined Bachelor of Advanced Studies is technically treated as a double degree, although perhaps not in the traditional sense. This means that, by nature, the Bachelor of Advanced Studies acts as an extension to the chosen standard degree (such as the Bachelor of Arts in this case), which in turn means that it cannot be taken on its own without a standard degree that it can extend and this makes sense.
The only avenue for taking the Bachelor of Advanced Studies would be to take an additional single degree that can be combined with it. However, a problem with such an approach is that it is highly impractical. This is because USyd offers the Bachelor of Laws as a degree to be combined with another, meaning that in such a case, and assuming that you receive offers for all programs, you would technically be enrolling in a total of four degrees. Another problem is whether doing so is possible to begin with. In theory, provided that you receive offers to the programs that you have applied for, and that you are somehow able to effectively manage a full-time load between all degrees, you may be able to enrol in a Bachelor of Arts/Bachelor of Laws as well as another single degree to be combined with the Bachelor of Advanced Studies. This could be classified as concurrent enrolment, which calls for the need to contact USyd if you were to consider such a path. Of course, it would be a good idea to contact USyd either way.
My personal opinion is that, provided that the workload is manageable, a combined law degree (for instance, a Bachelor of Commerce/Bachelor of Laws) would be superior to a standard degree to be combined with the Bachelor of Advanced Studies, since you would gain extensive knowledge relevant to two or more fields in a potentially better-structured degree sequence, as opposed to the perhaps slightly unusual structure, unless you are interested in research (including an Honours year), in which case the Bachelor of Advanced Studies may also be useful.
I hope this helps!