Do they generally make additional runs of these bundles, or is it limited to what's currently in circulation? I'm just trying to figure out how hard I want to push to get one of these.
No. In fact, I can't remember a time when Nintendo has done another print run (they even said doing another print run of the Fire Emblem system was illegal in Japan).
However, don't assume because there is a finite amount, that it will be worth something or be impossible to find. Some of these bundles stick around for weeks and in some cases months before selling out completely. One of the few exceptions was the Pikachu 3DS XL, since that one was the first, most limited (based off our anecdotal evidence) and had the best promotion / deal. Also, Nintendo seems more open to doing these in North America, so if you don't like the current systems and don't mind paying the additional money for a better design, you might want to wait.