The Sawyer Squeeze filter, at 3 oz. and very compact, is lighter than the fuel needed for lots of boiling sessions and takes a lot less time--you can drink the water right away. It can be used as a gravity filter, too.

Probably the next person on here will recommend chemical treatment. This is definitely a "Your Mileage May Vary" situation as long as you are using an effective treatment!
A filter is the fastest, though.

Just something to consider: To me, carrying a lightly-loaded and supportive backpack is much easier on my back than bicycling. Of course my back is not your back!

Enjoy your trip! It's a beautiful area!
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May your trails be crooked, winding, lonesome, dangerous, leading to the most amazing view--E. Abbey