We did one of the Mendenhall Glacier shuttles (through Juneautours) in 2016. Looks like prices have gone up $15 since then. Both Juneautours and the blue bus (glacier express through m&m tours) are $45/person roundtrip, (juneautours is $40 for kids 3-12). As I said, we did Juneautours glacier shuttle--it runs every 1/2 hour, get on at any time. Our drivers talked about Juneau and Tlingit culture for both directions of the drive....so it's slightly a tour while they're driving you the 25 minutes to the glacier.
The cheapest way would be to take the public bus, but the closest stop is 1 1/2 miles from the visitor center. Another option is to rent a car for the day and drive there yourself.