So, he had a gun trained on them all that time? I can’t imagine anybody wrangling three other guys for that long ;-)
https://www.nps.gov/thro/learn/historyculture/roosevelt-pursues-boat-thieves.htm
Above is the detailed story. It looks like I have some of the details wrong. Or - I read another version of it. He and two guys went after them and caught them. They were out for quite awhile. At one point waiting 9 days for the ice to clear from the river. (The guys were boat thieves).
Teddy had a shotgun to watch over the guys. Towards the end his two partners leave as they are running out of supplies. Teddy walks the guys in and spent 36 hours without sleep. At one point a wagon comes along, and the prisoners are in the wagon with Teddy walking behind and taking them into town.