Public Class MyForm

    Private scanner As New BarCodeScanner()

    Public Sub scanner_ReceivingEnd(ByVal sender as Object, ByVal e As BarCodeScanner.ScannerEventArgs) Handles scanner.ReceivingEnd

        ' Вот тут и возникает проблема, так как данное событие и реакция на него "находится" в "Рабочем" потоке,
        ' а элемент Me.TextBoxBarCode был, создан в "Основном" потоке.
        ' Как же сделать, так чтобы событие ReceivingEnd вызывалось еще не в "Рабочем", а уже в "Основном" потоке? 

        Me.TextBoxBarCode.Text = e.BarCode

    End Sub

End Class

Public Class BarCodeScanner

    Private WithEvents sPort As System.IO.Ports.SerialPort
    Private buffer As String = String.Empty

    Public Event ReceivingEnd(ByVal sender As Object, ByVal e As ScannerEventArgs)

    Public Sub New()

        Me.sPort = New System.IO.Ports.SerialPort(...)
        ...

    End Sub

    Private Sub EndOfReceive()

        RaiseEvent ReceivingEnd(Me, New ScannerEventArgs(buffer))

    End Sub

    Private Sub AttachData(ByVal data As String)

        Me.buffer &= data

    End Sub

    Private Sub sPort_DataReceived() Handles sPort.DataReceived

        Dim str As String = sPort.ReadExisting

        If (str = Chr(26), Me.EndRecived(), Me.AttachData(str))

    End Sub

    ...

End Class

Public Class ScannerEventArgs

    Private barCodeValue As String

    Public Sub New(ByVal barcode As String)

        Me.barCodeValue = barcode

    End Sub

    Public ReadOnly Property BarCode() As String
        Get
            Return barCodeValue
        End Get
    End Property

End Class

Private Sub EndOfReceive()
        RaiseEvent ReceivingEnd(Me, New ScannerEventArgs(buffer))
End Sub

Public Sub scanner_ReceivingEnd(ByVal sender as Object, ByVal e As BarCodeScanner.ScannerEventArgs) Handles scanner.ReceivingEnd
        Me.TextBoxBarCode.Text = e.BarCode
End Sub