Lyft seems to be doing okay, and don't underestimate targeted markets for upstart competition... If you can get most of the BnBs in say Sedona, Prescott and Payson Arizona to use your upstart service, you can grow from there, one targeted market at a time... local presence can be a significant advantage.
The textbook response would be a price war. Raise prices in uncompetitive cities and lower prices in at risk cities. This is one of the tools Standard Oil used to create its monopoly.
