Look into the Sawyer Mini or Squeeze. Hard to beat for $20. It's about all I've used for the last year.
https://www.amazon.com/dp/B00FA2RLX2/?tag=backcountrypo-20
I like having a couple 2 liter bags to bring water to camp to filter as needed...
I can't offer specific recommendations, but I've found more time is always better! There are so many alcoves and side canyons to explore. Sounds like a great trip. Hope you'll share pics when you get back!
I'll be out of service until next week. @Outdoor_Fool was close. How about if you take it?
We got lucky and caught a ride. Spent three nights on the BMT.
You've probably seen it, but here's a link to the ski trails map.
http://www.nps.gov/yell/planyourvisit/skiyellmaps.htm
And grooming info.
http://www.yellowstonenationalparklodges.com/things-to-do/winter-things-to-do/daily-ski-trail-status/