There is no way to convert a VBScript (.vbs file) into an executable (.exe file) because VBScript is not a compiled language. The process of converting source code into native executable code is called “compilation”, and it’s not supported by scripting languages like VBScript.
Certainly you can add your script to a self-extracting archive using something like WinZip, but all that will do is compress it. It’s doubtful that the file size will shrink noticeably, and since it’s a plain-text file to begin with, it’s really not necessary to compress it at all. The only purpose of a self-extracting archive is that decompression software (like WinZip) is not required on the end user’s computer to be able to extract or “decompress” the file. If it isn’t compressed in the first place, this is a moot point.
Alternatively, as you mentioned, there are ways to wrap VBScript code files in a standalone executable file, but these are just wrappers that automatically execute the script (in its current, uncompiled state) when the user double-clicks on the .exe file. I suppose that can have its benefits, but it doesn’t sound like what you’re looking for.
In order to truly convert your VBScript into an executable file, you’re going to have to rewrite it in another language that can be compiled. Visual Basic 6 (the latest version of VB, before the .NET Framework was introduced) is extremely similar in syntax to VBScript, but does support compiling to native code. If you move your VBScript code to VB 6, you can compile it into a native executable. Running the .exe file will require that the user has the VB 6 Run-time libraries installed, but they come built into most versions of Windows that are found now in the wild.
Alternatively, you could go ahead and make the jump to Visual Basic .NET, which remains somewhat similar in syntax to VB 6 and VBScript (although it won’t be anywhere near a cut-and-paste migration). VB.NET programs will also compile to an .exe file, but they require the .NET Framework runtime to be installed on the user’s computer. Fortunately, this has also become commonplace, and it can be easily redistributed if your users don’t happen to have it. You mentioned going this route in your question (porting your current script in to VB Express 2008, which uses VB.NET), but that you were getting a lot of errors. That’s what I mean about it being far from a cut-and-paste migration. There are some huge differences between VB 6/VBScript and VB.NET, despite some superficial syntactical similarities. If you want help migrating over your VBScript, you could post a question here on Stack Overflow. Ultimately, this is probably the best way to do what you want, but I can’t promise you that it will be simple.