How do I add a dev wordpress installation (diff version)

I had to uninstall the chat plugin because the current version of the site 3.2.1 just doesn't support it. I was able to cobble together a different solution, but would really like to bring the WP installation up to 3.8 so I could use it and some other cool stuff I see around here.

However, unless there's a pretty easy way to do that without mucking everything up, shopping cart, personalized theme (not developed by me) with extensive CSS and php modifications, I was thinking I'd like to set up a parallel installation, sort of a dev environment.

The current site uses wp eCommerce with gold cart, and I'd like to port all that data (products, pricing, images, etc) over to the new install. Can I install another, fresh version of WP in a folder other than root of public html and point it to the existing database? If not, then perhaps I can just do a dump from that database and import into the new one?

The site is on BlueHost, any ideas of how to best accomplish this? Once I have the new blog up and running and working the way we want, Then I could either move it into root and touch all references to the folder (changing them back to root of public html), or just do a redirect to the new install folder when a person hits the site.