Have you tried:
Application.DisplayAlerts = False
Like:
Application.DisplayAlerts = False   
 ActiveWorkbook.EnvelopeVisible = True
        With ActiveSheet.MailEnvelope
            .Introduction = "Rejected Payments Report"
            .Item.To = Sheets("out").Range("bm370").Value
            .Item.Subject = "Rejected Payments Report [DLM=For-Official-Use-Only]"
            .Item.Send
        End With
    ActiveWorkbook.EnvelopeVisible = False
    Application.DisplayAlerts = True
Hope this helps