Please ensure that the following is enabled:
In System, Options, Purchase Ledger Options
in the Transactions tab, check the option Update Supplier with Expense User Bank Details.
Synchronise expenses
Note: Bank details are only updated for Supplier records already linked to a claimant at the time of download, and also only where that claimant has an expense waiting to be posted at the time of synchronisation (whether previously or freshly synchronised)