I am assuming you are talking about DateRcv column.
You would the actual date time like this:
getdate()
So, if DateRcv needs to get updated when you run that insert query, your insert would be like this:
Insert Into [Billing Automation Processes].dbo.billrunstatustable (InvoicesRecdDate , DateRcv)
Select Max(InvoiceDate), getdate() from bill.dbo.Invoices
Let me know, if this does not work for you.