Short answer
Usually no. Section 48 and no further stay rules do not usually stop you from making a valid bridging visa application, because a bridging visa is not a substantive visa.
Section 48 can limit the visa classes you may apply for in Australia after a visa refusal or cancellation. The limited classes include all bridging visa classes.
No further stay rules, such as conditions 8503, 8534 or 8535, also do not prevent you from making a valid bridging visa application. This is because a bridging visa is not a substantive visa.
This does not mean every bridging visa application will be granted. The person still needs to meet the validity and grant criteria for the bridging visa type.