We will be in Aspen the last week of May. Will the local buses to Highlands and onward to Maroon Bells be running midweek? Will the gondola to the top of Aspen Mountain be running midweek as well?

The Roaring Fork bus service runs 365 days a year.
http://www.rfta.com/
If the hotels in Aspen are too expensive you can stay in Glenwood Springs. There is a gondola ride up from Glenwood Springs to the Cavern.

Here is the gondola schedule for Aspen.

SUMMER OPERATIONS:
Weekends: May 28-30, June 4-5, June 11-12
Daily: June 18 – September 5, 2016
Silver Queen Gondola Hours: 10 am – 4 pm (last ride down at 4:30 pm)

And, Snowmass:

Daily: June 25 – September 5, 2016
Weekends: September 10-11, 17-18, 24-25 and October 1-2
Elk Camp Gondola Hours: 10 am – 4 pm (last ride down at 4:30 pm)
Elk Camp Chairlift Hours: 10 am – 3 pm (last ride down at 3:15 pm)

As you can see that you time period will be somewhat dead because of the change over from winter skiing to summer activity. Full summer operation get started around mid June. The bus is scheduled to run from mid June through Oct each year. I cannot remember is car access is allowed when the buses are not running. And, depending on snow conditions, the road to the park might not be open. You might try this web site

http://www.aspenchamber.org/explore-...s/maroon-bells

PS - the Roaring Fork bus service has nothing to do with the bus to the maroon bells. That service runs the valley between Aspen and Glenwood Springs.

I don't know if they run the service all year long but on the video of one of the Roaring Fork buses, it said Maroon Bells on the overhead display.

That is the Maroon Bells stop. That is not the bus that takes you to the Maroon Bells from the parking lot.