There is one company that runs shuttles between GYE (Guayaquil) and Salinas called "Ruta del Sol". They have offices in both locations. In GYE they are behind the Ramada Hotel in GYE and in Salinas next to Bariloche Café on the Malecón.
They operate 7 days/week from 8am-6pm. After/before-hours pick-ups available at higher rate. Per person shared vehicle rate is $10 one way. Private car $35. Private van $90.
They say supposedly no pets and claim to have a luggage limit (but they typically will just charge you extra for it).
No website; and limited (if any) English spoken. Call for more info and schedules:
GYE office 04/230-2984
SAL office 04/277-0358
They also pick up/drop off in/around the Salinas area, such as Anconcito, Punta Blanca, Ballenita, etc.