Yes, you can import transactions from your ASB Bank accounts.
Firstly, on the website, create a Transaction List and export it to a QIF formatted file (make sure its date format is in dd/mm/yyyy (sometimes referred to as QIF - Quicken AUS)).
then inside yoru company file go to Banking > Import Bank Statement and follow the prompts to bring in the transactions into the Online Banking Centre. From there you can allocate them to your ledgers.
Here are a few video guides to help you continue with the process: