Not in front of my dev machine but I think the error you will get is file not found.
You have asked your program to execute run.bat but not told it where run.bat is actually stored.
Try this:
Dim path As String
path = System.IO.Path.GetDirectoryName( _
System.Reflection.Assembly.GetExecutingAssembly().GetName().CodeBase)
Process.start(path & "\Run.bat")
You may not need the \
The path will be set wherever the exe is ran from, so the batch file will have to be in the same folder. EG: c:\Myprog\Myexe.exe and c:\Myprog\Run.bat