Please refer to the attached gif file.

Workaround: handle the SelectedIndexChanged event and update the DataBoundItem programmatically:

Dim dt As New DataTable
Dim bs As New BindingSource
Sub New()

    InitializeComponent()
    AddHandler Me.RadDataEntry1.EditorInitializing, AddressOf EditorInitializing

    dt.Columns.Add("Id", GetType(Integer))
    dt.Columns.Add("Name", GetType(String))
    dt.Columns.Add("Type", GetType(DeliveryType))

    dt.Rows.Add(1, "Item1", DeliveryType.Type2)
    dt.Rows.Add(2, "Item2", DeliveryType.Type3)
    dt.Rows.Add(3, "Item3", DeliveryType.Type1)

    bs.DataSource = dt
    Me.RadDataEntry1.DataSource = bs
    Me.RadBindingNavigator1.BindingSource = bs
End Sub

Public Enum DeliveryType
    Type1 = 0
    Type2 = 1
    Type3 = 2
End Enum

Private Sub EditorInitializing(sender As Object, e As Telerik.WinControls.UI.EditorInitializingEventArgs)
    Dim ddl As RadDropDownList = TryCast(e.Editor, RadDropDownList)
    If ddl IsNot Nothing Then
        AddHandler ddl.SelectedIndexChanged, AddressOf SelectedIndexChanged
    End If
End Sub

Private Sub SelectedIndexChanged(sender As Object, e As Data.PositionChangedEventArgs)
    Dim dataRowView As DataRowView = TryCast(bs.Current, DataRowView)
    dataRowView.Row("Type") = e.Position
End Sub