I will also suggest doing it in sections. I have done 3 one week sections.
First was in 2018 at 65 from Banff to Whitefish with ACA.

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In 2019 from Helena to Whitefish with two others I met on the 2018 trip. We encountered a woman riding her Atlantis going southbound. She was not a happy camper with her Atlantis but I can't remember why at the moment. I think maybe she was not satisfied with her tires.
Third was in 2025 at 72 from Jackson, WY to Rawlins. We started as 3, one from the 2018 and 2019 trips, and another I met on the ACA North Star in 2022. Two of us were going to take 4 weeks to ride to Salida but I bailed after a week when we had already done half the planned distance. Aside from being six years older than my last trip on GDMBR (and the other two riders), I had no time to acclimate to the much higher altitudes and the longer distances we were riding. I had flown in from San Diego - sea level.

All three trips were on my Atlantis with the same 50mm Schwalbe (Mondial?) tires each time. When I quit this past summer, I felt quite defeated and thought I was too old and done with this but, when I got home and realized we had done more mileage, more climbing at much higher altitudes than on my previous rides I again hold hope of doing another section yet. Two of us are talking about it. On our third day we rode 55 miles with over 5k ft of climbing on washboarded gravel at over 8k feet, peaking over 9.6k ft. I did a lot of pushing that day, saw some of the most beautiful country I have ever seen, and experienced a level of exhaustion I have never before experienced. I was literally panting for air while descending.
One will encounter many other riders of many ages from all over the world on the GDMBR. This past year we encountered two women from New Zealand who were riding the whole thing together from South to North. We were also passed by many of the riders in the race. Naturally, they were traveling much lighter than we were.
As far as bears are concerned, we rode with bear spray and tried to practice safe practices in camp. On the ACA trip, a grizzly with two cubs wandered through the camp ground. It was unnerving but nothing bad happened. Perhaps more alarming was when one guy noticed in his rear view mirror something following him. He stopped to see what it was - a mountain lion. Another came up behind the lion and, sandwiched, it decided to leave the scene. The other trips were uneventful with respect to wildlife, which is not to say we weren't cautioned of recent activity. I think I've heard that south of Rawlins, Grizzlies are not a threat.
Bill S
San Diego