Does more suds mean more clean?

The purpose of laundry detergents is to trap and remove dirt, but in order for adequate cleaning performance, the trapped soil needs to be completely removed. Too much soap doesn't allow optimal cleaning performance. So whether you're using regular, HE, and/or green detergents, more suds don't mean more cleaning power.

Do bubbles equal clean?

Bubbles can serve as a sort of indicator of the concentration of soap in the water, which does effect how clean stuff gets. However this is only a rough indicator, and isn't really reliable. Beyond that, there's really no correlation between bubbles and how clean anything gets.