When are you going to be here? It's still pretty snowy up in Summit County - if you're here in the next few weeks, the Glenwood option might be better. It's *way* more than an hour of riding. On the East side of Glenwood, it's an amazing piece of bike path, but it is right under the freeway. You're not right next to the cars, but it's not exactly a wilderness experience. Also, you're in a canyon (a spectacular one) rather than on a mountain pass. From Glenwood SPrings you head south out of town towards Carbondale, that part is pretty flat, in a moderately wide open valley. Then you can hang a left and go up to Aspen, gently climbing.
SO, that bike path is a really nice bike path, and if path is what you want, it's worth doing. But, it is a solid 3 hour drive, so unless you were planning to go out there for a couple of days (good idea, by the way) I wouldn't say it's worth it. I would say the same about the Dillon/Frisco paths, which wind around the lake.
The other think you could do would be go to the Glenwood path one day, then out to Grand Junction the other day and ride the Colorado National Monument loop - about 35 miles and 2500 feet of climbing, great scenery, lower altitude so it's good if you are coming here before the snow melts in Summit County (Dillon/Frisco). There's also an out-and-back from Aspen to Maroon Bells, that I haven't done, but that I hear is fantastic and is closed to auto traffic except a shuttle bus, so if you are looking for car-free riding, that might do the trick. You might want to check on seasonality of that road.