Nomenclature - Common vs IUPAC Names and Alphabetical Priorities
No, 2,2-dimethyl-7-(1-methylethyl)bicyclo[3.2.0]heptane is not an acceptable name.  Like the rule you quoted says, start numbering at a bridgehead carbon and first pass through the largest ring (in this case the 5-membered ring) and number that ring so that a substituent will have the lowest number.  So this molecule would be named 2-isopropyl-7,7-dimethyl-bicyclo[3.2.0]heptane.  Usage of "1-methylethyl" is not acceptable.  If you weren't going to use the term "isopropyl", you could call the fragment "2-propyl". So you could write 2-(2-propyl)-7,7-dimethyl-bicyclo[3.2.0]heptane, but the term "isopropyl" is much more common usage.

Edit: After reading Greg E's comment, I looked around the internet and found that "1-methylethyl" is both correct and the official IUPAC name.  Here is a paraphrasing of the relevant IUPAC rule...

These groups (those attached off the main chain) are always numbered so that the point of attachment to the rest of the molecule is C1, with the longest continuous chain beginning from the point of attachment taken as the parent. 

Then all sites I visited would add something like this...

"For historical reasons, some of the simpler branched-chain alkyl groups also have nonsystematic (or common, or trivial) names."

Most of these sites seemed to (strongly) favor the trivial name.  As one site put it, "Common names are used because they are easier to say, shorter, and save paper
and ink in scientific publications when they have to be used repeatedly in manuscripts."