Seat
Shared shuttle is usually the simplest fit for one or two people who want the return handled.
Red Rocks feeder page
Red Rocks shuttle cost: what you are really paying for
Direct answer
A Red Rocks shuttle usually costs more than the cheapest possible ride in, but it buys a planned return after the show. The value is not just the seat. It is avoiding parking decisions, surge pricing, and pickup uncertainty.
Group
Private transportation can make more sense when a full group wants one vehicle and door-to-door control.
Hidden cost
Uber can look cheaper before the show and get weaker after the encore when everyone requests rides.
Recommendation
If you are comparing cost, compare the full night, not just the ride there. For most visitors without a sober driver, the shared shuttle is the safer default.