I'm currently trying to advance the chapter 2 story. I found one ninja, and now the current goal thing says "wait for events to unfold". Is there anything I can do to speed it along?
You can hunt the other two ninjas, who will be in the other two districts. A fixed location for each ninja's first battle; a random one for battles 2 & 3.
If you meant you met the blue-haired Suzume, then you may need to visit more locations to continue (ending with
Spoiler
the Arena
.
You will get called in to the princess
Spoiler
when you have met all three ninjas once
.
And keep in mind that the 3rd meeting for each will be unwinnable, but required for story progress.