Spent 4 days there in January 2000: two nights outside the park in Study Butte and two nights inside at the lodge. The lodging outside the park isn't that great, and I'd recommend staying inside for you entire visit.
It does take forever to get to -- the nearest decent airport is ELP, 300 miles away. So you have to really want to go there, and the effort required means you want to spend some time while you arrive. Fortunately, the drive on the way in (Texas 118) is one of the more interesting roads I've been on.
If you hike there are plenty of ways to spend 5-6 days, but otherwise you might get bored sooner. There ain't much in the way of dining options; one restaurant inside the park and a diner-type place or two outside. Big Bend is NOT like a lot of parks that have miles of crass commercialism right outside the gate, for better and for worse.
Peak time is March and April, when kids are on break, desert flowers are blooming and the weather is ideal. The lodge fills up two years in advance for the spring, but the rest of the year should be quite uncrowded. Summer is too hot, but the January I went had perfect hiking weather.
Definitely worth visiting if you want to make the committment. I can be more specific as to hikes and other activities if you want.