When you have to provide credentials in non-interactive mode, you can create a PSCredential object in the following way.
$secpasswd = ConvertTo-SecureString "PlainTextPassword" -AsPlainText -Force
$yourcreds = New-Object System.Management.Automation.PSCredential ("username", $secpasswd)
$Job = Start-BitsTransfer `
-DisplayName DMFweeklytrans `
-ProxyUsage AutoDetect `
-Source https://dmf.ntis.gov/dmldata/weekly/WA$date `
-Destination D:\Test.txt `
-Authentication Basic `
-Credential $yourcreds `
-Asynchronous