Please do not be confused with the type of visa that you are going to apply for Competence program or IRON program in Australia.
You an an option for either subclass 575 visa, which is a student visa for non-award courses. Since the bridging program belongs to the non-award course, so you can choose this option. There are some forums that i have had read giving advices of getting other types of student visa. Please note that student visa in Australia has different types and to avoid your application from being denied, kindly read more informations regarding visas in Australian Embassy Website.
The second option you can have is the short stay visa subclass 456. Kindly read it on this link, by clicking on the word CLICK HERE
Please be aware that, there are some institutions that requires you to have a specific type of visa, like for instance the VCHN in Melbourne, Victoria, where they required all those student that will take the bridging program in their institution to have a business short stay visa.