Based on the official website, these are the system requirements for Bluestacks:
OS: Windows 10, Windows 8.1, Windows 8, Windows 7, Windows Vista SP2 , Windows XP SP3 (32-bit only)
You must be an Administrator on your PC.
Your PC must have at least 2GB of RAM/main memory. (Note that having 2GB or more disk space is not a substitute for RAM)
Your PC must have 4GB of disk space available for storing Android apps / games and their data.
The drivers for your PC's graphics drivers should be updated for compatibility with BlueStacks as described in the following post
The PC must have a broadband connection to access games, accounts and related content
As you can see, Windows Vista SP2 is a supported operating system, which means you can install it. Access the application's page at Software Informer to obtain the package.