Yes, there an option to save your invoice format print settings in BUSY, to enable this need to follow the below step:
Step 1: Go to Administration.
Step 2: Choose Configuration.
Step 3: Access Voucher Series Configuration.
Step 4: Select Sales Invoice.
Step 5: Pick your series.
Step 6: Under configuration, enable Print Sales Invoice after Saving.
Step 7: Specify the number of formats and choose your preferred format.
By doing this, you won't need to select print options every time you generate an invoice.