I think renting the car is the best (most economical) option. Alyeska provides the following information:
https://www.alyeskaresort.com/resort...transportation
If you don't want to rent a car then contact the concierge. Uber and Lyft both appear to be about $80 at the moment. Cabs are usually about $95 - 100. Shuttles may be over $100 each way. There used to be a ski bus on weekends ibut I don't know if it still operates or what the cost is.