What does data density mean? Having as much data as possible per unit of space?

Yes, exactly. E.g., a datagrid showing, say, only a dozen rows in a full screen browser on a 1080p screen, when it can easily show 2-3x that many and still be perfectly readable. For entertainment/marketing/whatever sites, a dozen rows may be fine, but for a business app, it's frustrating. And sure you can just zoom out, but you still have the same data-to-whitespace ratio, just with unreadably small text.

It also seems like Bootstrap (at least previous versions) makes it unnecessarily hard to get good data density without heavily customized CSS - something that kind of defeats the purpose of using Bootstrap in a business app.

Yea, I'm having the same problem with a React-MaterialUI business dashboard that I'm building.

Is there a good framework for this?

I’m using BlueprintJS for a startup I’m working on and it’s great for this reason, components that are purpose built for data density.

https://blueprintjs.com/

It is not meant for mobile but can be made to work. If you want a mobile first experience I’d use something else though.