The Shulhan Aruch (OC 178) rules that if one is in transit, the Halachot of Shinui Makom, changing locations while eating, do not apply. For example, if a person drinks a bottle of water throughout the duration of a bike ride, changing locations does not require a new Beracha every block. The same would apply to people who eat while walking in the street. The original Beracha of Shehakol recited at the beginning of the trip covers the rest of the eating or drinking throughout the route.
The Yalkut Yosef English Edition presents a Hidush that even if he made the original Beracha in his house on his way out, he would not have to make a new Beracha when he steps outside and wants to continue drinking. For example, a person wants to take a sip of coffee in his house before he continues out on his way to work. This applies to cases when the Beracha made in the house was recited "on the go," but if he made the Beracha while seated, and then he leaves the house, he must make a new Beracha in his new location.
SUMMARY
If one is in transit, the original Beracha exempts the entire eating or drinking, even though he is constantly changing locations. This applies even if he recited the original Beracha "on the go" in his house.
