My wife and I stayed at Fishing Bridge for 7 days this past June. Then went and stayed 7 days at the Grand Tetons, then 7 Days in Glacier, then own to Mt. Rushmore in SD among other places. Between all the places we went and day trips we went through every entrance of Yellowstone. It really depends on where you are coming from, or going to after the park.
Staying at Fishing Bridge is nice, but it is a no frills rv park, and it is about 60 miles one way to reach Old Faithful. Also, keep in mind that 1) Fishing Bridge is the only Full Hook Up facility within the part, 2) Pretty much every entrance requires at least 20 miles of driving until you reach any 'attractions' so to say, and 3) There is fuel inside the park, and it was over $4 when we were there.
Staying at Fishing Bridge was ok for us, but there was a lot of time spent in the truck just getting too and from various places. We could have spent way more than 7 days there, it just depends on what you want to see. If you want to stay at Fishing Bridge, be sure you book it well in advance. I booked it in January, and at that point there was only one full week available for us to stay all summer. So, we built our trip around that week.
Edit: The West Entrance was by far the busiest entrance we went through! LOOONNNGGG lines to get in!