Here is how you would do it, you won't need to create a recordset object since it is an update stored procedure:
'Set the connection
'...............
'Set the command
DIM cmd
SET cmd = Server.CreateObject("ADODB.Command")
SET cmd.ActiveConnection = Conn
'Prepare the stored procedure
cmd.CommandText = "apUpdateBill"
cmd.CommandType = 4 'adCmdStoredProc
cmd.Parameters("@RECORD_NUMBER") = Request.Form("Record_Number")
cmd.Parameters("@ErrorType") = Request.Form("ErrorType")
cmd.Parameters("@INSURANCE_CODE") = Request.Form("INSURANCE_CODE")
cmd.Parameters("@CompanyId") = Request.Form("CompanyID")
cmd.Parameters("@INS_ID_NUM") = Request.Form("INS_ID_NUM")
'Execute the stored procedure
'This returns recordset but you dont need it
cmd.Execute
Conn.Close
SET Conn = Nothing