I would create a function, that took a string as it's parameter, and returned a value that was the digits added together.
Private Function AddDigits(s As String) As Integer
Dim result As Integer = 0
For Each c As Char In s
If [Char].IsDigit(c) Then
result += AscW(c - "0"C)
End If
Next
Return result
End Function
I would then use a loop to call this until I had only one digit left:
Dim str As String = "123324::34"
Dim res As Integer = 0
Do
res = AddDigits(str)
str = res.ToString()
Loop While res >= 10
myTextBox.Text = str