Final answer:
The ferry was traveling west from Seattle to reach Bainbridge Island across the Puget Sound.
Step-by-step explanation:
As the ferry was on the way to Bainbridge Island, it was traveling west from Seattle across the Puget Sound. Bainbridge Island is located to the west of Seattle, and the ferries that connect these two locations via the water route typically head westward. This direction allows passengers to enjoy views of the Olympic Peninsula as they approach the island. In the passage provided, it is mentioned that steamboats traveling to Philadelphia from Baltimore went up the bay in a north-easterly direction when they reached North Point. This information suggests that the ferry traveling to Bainbridge Island was also going in the same direction.