BuddyPress.org

I would like to install buddypress onto my existing wordpress install (regular wordpress not wordpress mu).

At this time, BuddyPress only works with WPMU 2.7.1. You cannot use it with single-version WordPress.

How would I upgrade this to a wordpress mu/buddypress install?

https://mu.wordpress.org/forums/topic.php?id=11126

will this integrate with my current wordpress theme

No. You will either need to use the standard BuddyPress themes that come with the package, or update your custom themes as detailed here: https://codex.buddypress.org/getting-started/installing-buddypress/upgrading-from-rc-1/