Will it work on Windows 7 Ultimate 64 bit?
Yes, Bluestacks will work on Windows 7 as long as the requirements listed on the official websites are met: https://bluestacks.zendesk.com/hc/en-us/articles/201691647-Windows-8-1-8-7-installation-requirements-
It's highly recommended that you have a capable GPU card to enjoy full graphic processing power.
Here's an alternative if you can't work with Bluestacks: http://www.memuplay.com/