Yes!  You can definitely use Bambino while traveling. In order to create a request in a new city/town you simply need to change your home address in the app before creating the new request.  To do this select:

My Account > My Profile > Basic Information > (update the Home Address) > Save

-next select (as usual)-

Bookings > Create Request > Enter sit date/time, children and in 'Special Instructions' indicate you are in town visiting > the app will populate with a selection of local sitters.  You might also see a local Community Coordinator banner along the bottom of the homepage if it is an established community.  Please reach out to the local Community Coordinator if you would like sitter recommendations or help with your request. 

Once you've confirmed a sitter you can go back in your profile and change your address back to your home address.  The address you had entered for your new destination will remain in the reservation for the sitter.