Mr De Vietri said Prince had claimed the suitcases were given to her on a trip to Kenya, where her mission does charity work, by a stranger known only as "Mummy Rose".
Defence counsel Michael Burrows said importing drugs did not fit with Prince's background.
"How does a person go from being CEO of an international Christian mission to being an international drug trafficker?" Mr Burrows asked.
He said Prince's bags had gone missing in Singapore for 24 hours and no one had explained what happened to them then.
It also did not fit that a person carrying drugs into Australia would travel via Singapore, where the death penalty existed for such crimes, Mr Burrows said. One of Prince's two passports was invalid and related to her changed name after she remarried, he added.
Mr Burrows said the credit cards were in different names because one belonged to the defendant's husband, one was her mother's and one included her maiden name.
In rejecting the bail application, Mr Neill said he had doubts over claims Prince would carry bags from an unknown stranger into Australia.
"I regard that, without further explanation, as quite extraordinary," Mr Neill said.
Prince will reappear in court on August 21.
- AAP
