Updates, dependencies, offline development, etc. Not really a node.js thing (though bower itself can be installed via npm), it's specifically targeting front-end development.
The debate over CDN vs. local is debated on all levels. Usually CDN is faster due to cached files, but what I consider the "best" approach is to use a CDN for most everything with local fallback (yes, you can use bower packages for the fallback if you please).
Good decision since Xamarin is much more native when compared to PhoneGap/Cordova (Titanium is another thing I've been looking at). The student discounts for $99/year/platform should be the normal price.