It's a few short blocks from the Amtrak station to the court house/city hall stop in Glenwood Springs. Not all VelociRFTA routes go through Glenwood but a fair amount of them do, and the rest stop/start at the South Glenwood BRT station.
Amtrak from Denver is scheduled to get into Glenwood Springs at 1:53 pm daily. Based on RFTA's Fall schedule there's an Aspen bound VelociRFTA which should get to the court house stop around 1:57, if your friend misses that there's a local valley bus to Aspen (upvalley) that should arrive around 2:09, another upvalley VelociRFTA should arrive around 2:17, followed by another upvalley VelociRFTA around 2:29, and then another local upvalley route should arrive at the courthouse around 2:39.
NOTE: Added 9 minutes to the time the buses leave the Glenwood Park and Ride in order to figure out the times they get to the courthouse stop which isn't listed in the schedule.
EDIT: It looks my info will be inaccurate in December. Although the frequency looks similar it looks like RFTA is slightly
tweaking the schedule on thanksgiving, not sure how long their Fall Shoulder Season lasts though so I guess it could change again. Also I found this
realtime map which is much more helpful than the RFTA PDFs for finding stops (BRT = Velocirfta and VAL = Valley local).