Ontario International Airport: This is the sensible commercial airport for Big Bear. Rent a car at ONT and take the mountain route via the Inland Empire; allow roughly 2–2.5 hours in clear, non-peak conditions, much longer on ski weekends or in storms. There is no airport-to-village public transfer worth building a trip around; a one-way rideshare is expensive and unreliable for the return.
Palm Springs International Airport: A workable but less convenient alternative, best only if fares or your wider itinerary make it worthwhile. Rent a car; expect roughly 2.5–3.5 hours depending on the route and mountain conditions. Do not count on a practical direct public-transport connection.
Big Bear City Airport: A small general-aviation airport at the east end of the lake, useful only to private pilots. Arrange a rental car or a pre-booked local ride before landing; the airport is not in walkable Big Bear Lake village territory.