It was the polar opposite of the life he imagined for himself, a life of wandering and exploration through country unknown. (1.6.35)
Initially, Bridger tries to satiate his thirst for adventure by working on the Mississippi, but that proves to be a wash (pun totally intended). By now, people have traveled up and down the Mississippi a million times—Bridger wants to do something new.
The boy came to believe that going west was [...] a part of his soul, a missing ounce that could only be made whole on some far-off mountain or plain. (1.6.34)
Bridger isn't messing around, people. Although he's spent his entire life chasing excitement and adventure, they always seem just out of reach. That's not true on the frontier. On the frontier, simply going from Point A to Point B is a serious undertaking, one requiring bravery, skill, and a hearty sense of adventure.
Chapter 7: September 2, 1823 – Morning
The men knew little about Texas, but Glass found himself suddenly exhilarated, about to embark without compass into the interior of the continent. (1.7.68)
Only somebody like Glass would be enthused about being abandoned in the middle of a Texas desert, but we wouldn't have it any other way. After all, he's found exactly what he's been searching for his entire life: an uncharted place where he can make his own way, free of all constraints.
Glass had come to view the sea, which he once embraced as synonymous with freedom, as no more than the confining parameters of small ships. (1.7.57)
Glass first tries to scratch his exploration itch by becoming a sailor. And sure, that works for a while, but the experience quickly becomes claustrophobic. So if Glass can't find adventure on the sea, and Bridger can't find it on the Mississippi, then where can they find it?
The source of Hugh's fascination lay not in the abstract representation of places, but rather in the places themselves, and above all the vast masses marked terra incognita. (1.7.17)
As a youngster, Hugh Glass becomes totally obsessed with cartography. As it happens, however, this interest doesn't derive from the act of actually making maps—it's rooted in the mysterious places those maps depict.
Chapter 15: October 9, 1823
Kiowa understood early in his career that his trade dealt not only in goods, but also in information. (1.15.94)
Like Bridger and Glass, Kiowa Brazeau sees life on the frontier as a learning experience. That actually explains why he and Glass make such fast friends: they love adventure and exploration more than anything else.
Chapter 16: November 29, 1823
With the exception of Charbonneau [...] the voyageurs approached each waking moment with an infallibly cloudless optimism. (2.16.15)
The voyageurs are a unique bunch, and though their chatty style differs from the hard-nosed one favored by Glass, they attack the unknown with an equally passionate aplomb. Although he had wanted to travel alone, Glass finds himself grateful for their company.
Glass came quickly to understand the odd affection of voyageurs for their craft. It was [...] a partnership between the men who propelled the boat and the boat that propelled the men. (2.16.5)
The voyageurs have a very romantic notion of exploration. We can see this embodied in their relationship with their boat, which Glass likens to a "marriage," as well as in their warm relationships with each other. In many ways, their feelings of camaraderie and togetherness only heighten their experiences exploring the wild unknown.
Chapter 22: February 27, 1824
Finally Glass said simply, "Follow your own lead, Bridger." Then he turned back to the horse. (2.22.49)
Good advice. When he was with Fitzgerald, Bridger played second fiddle—mostly due to his own insecurity. But he was selling himself short. He might not look like much, but Bridger has a real explorer inside of him.
Chapter 28: May 7, 1824
He raised his eyes to a horizon carved from snowy mountain peaks. [...] He could climb up there if he wanted. Climb up there and touch the horizon, jump across and find the next. (2.28.23)
See what we're talking about? It's actually important to note that The Revenant doesn't end with Glass—it ends with Bridger setting off on his own. That's a big deal. While Glass has already lived a full life, he has basically become the person he's going to become, while Bridger still has a huge potential for growth. And guess what? The frontier is the only place where that potential is going to be reached.