Solution 1:

It turns out to get this application working under VBScript, I had to do two things.

  1. Run RegAsm.exe to register the DLLs.
  2. Run the C:\Windows\SysWOW64\cscript.exe to run my VBScript.

If these don't work, check out the other answer here about enabling 32-bit applications in IIS.

Solution 2:

It's also worth checking that you've got "Enable 32-bit Applications" set to True in the advanced settings of the DefaultAppPool within IIS.