There is a Selenium webdriver created that works with VB.NET, VBA, and VBScript. Download and install the exe.
There are also lots of example scripts that show loading different browser types or in your case Chrome. Once loaded you just need to program what elements to navigate and click after loading your specific URL.
There might be other ways to launch and run commands against the web browser using VBScript. This is just one way.
SeleniumBasic v2.0.9.0 created by Florent Breheret and open source via git hub.
A Selenium based browser automation framework for VB.Net, Visual Basic Applications and VBScript
Script Example:
Set driver = CreateObject("Selenium.ChromeDriver")
driver.Start
WScript.Echo "Click OK to quit"
driver.Quit
Here is the official SELENIUM page: selenium main page
UPDATE:
Here is a second option that is based on the same concept , but implemented a little different. I am not sure it meets your needs , but thought I would include it as another example.
VBS WebDriver
Examples using the VBS WebDriver which is intended to provide a simple binding for Selenium 2. The bindings include the full functionality of Selenium 2 (WebDriver).