It's a balancing act to be honest.
With a RAW capture - and a purely reflective scene (as the background is) you generally don't need to worry too much about under-exposing. If you hit the subject with the same amount of light again (so she's illuminated 50% by ambient & 50% by flash) then you're only over-exposing her by 1 stop, which a RAW exposure will easily handle ... from there you reduce EVERYTHING to a correct exposure and "hey presto" you've dropped the background back by a stop.
Some further notes on that though ...
- Usually I apply a vignette when then gives the illusion of better targeted lighting
- The effectiveness of your fill light is going to depend on a number of things like how far away it is and the F-Stop you're shooting at. With the right equipment you can have the flash operate in HSS mode which means you can get your shutterspeed above X-Sync - which means you can get your aperture open wider - which means you can throw your background out of focus more - which is generally a good thing. With HSS mode you lose another stop from the flash though. To be honest, I use 4 flashes in a 30" x 30" softbox for this kind of work, so power isn't a problem (the mount is called a 4-Square) (from Lightware) and I used to trigger the lights via a PocketWizard TT1 + 4x TT5 combination, but I've now moved to the new 600EX-RT models and have a SST-E3-RT arriving in a few days).
You need to be VERY careful about under-exposing the background in camera, because the flash will ALWAYS add light to the foreground, and you and up with too high of a contrast ratio - which makes the light VERY directional, and usually not very flattering.