What you can do (if you're not already doing it) Implement a quick-start feature that simplifies the process: users input a date they need coverage, and the system proactively suggests compatible verified-only sitters with auto-generated message templates.
Introduce push notifications that remind users to reach out to nearby matches or highlight new pet parents in their area.
Also you can consider hosting local meet-and-greet events (since you're set in the Bay Area), partnering with local pet shops or parks to build trust.
Adding a group chat feature for local neighborhoods (i.e. for a city, or a neighborhood) can foster communication and trust.
You can add "premium sitters" that can gain money if they do some specific things like in person verification, they have a big fenced garden or something else. They will cost money to book them.