I'm actually going to give you 3 routes. Each one has its charms and problems. For convenience, I've started each route from Civic Center Park in Denver.

First is a route that will put you back on the TransAm as quickly as possible which is Denver to Walden via Loveland Pass. This route follows I-70 on secondary roads and bike paths to Dillion which puts you onto CO 9 which is the TransAm route. It's 180 miles and requires climbing up to Loveland Pass which is 11,900 feet. It's a pretty long slog up a fairly steep valley. You have to ride on I-70 for about 2 miles from the Genessee exit to the Evergreen exit but you are on side roads the rest of the way. Loveland Pass has some traffic but most of the traffic going to Summit County goes via the Eisenhower Tunnel so traffic is a bit lower than the next route.

Which is Denver toWalden via Berthoud Pass. This route is the shortest route at 145 miles and shares a fair amount of the same route as the Loveland Pass route. You don't have to climb out of Georgetown...a nasty little climb... but Berthoud Pass is the only route over to Winter Park and points north. It has a lot of traffic compared to Loveland. It's doable but it's going to be a more stressful ride.

Because of the mountains to the west, there are only a few places where you can cross on a road bike. The next one is over Trail Ridge Road. This is the highest route...12,183 feet...and that extra 300 or 400 feet take its toll. Trail Ridge itself is a nice road. Traffic can be high but the speed is low and the ride is fairly stress free. Getting to Trail Ridge isn't all that easy however. First you have to cross Denver and get to Boulder. That's not the easiest thing to do and you are cutting across the most populated part of Colorado. The ride out of Lyons is also narrow with a fair amount of traffic on a steep climb. Trail Ridge is very lovely but the hassle of getting there may not be worth the trouble. There are a couple of options to US36 like St Vrain Canyon (CO 7) but that is longer and steeper.

The last route is through Fort Collins over Cameron Pass. This route is the longest and, like the route to Boulder, takes you right across the Metro Denver area. It's nice enough riding but it can get hot out there on the plains and it's not all that pretty until you start up Poudre Canyon. It is the lowest crossing point, however.

Of the 4 routes, it would be hard to choose. Loveland Pass is actually a pretty ride once you get past Idaho Springs/Georgetown. It would probably be the lowest traffic choice once you start to cross the pass. Berthoud Pass is the shortest but would probably have the highest amount of traffic. It's pretty but not stunning. Trail Ridge is one of those things that a great bucket list item and is gorgeous but you have to deal with the ugly stepsister of getting there first. Cameron Pass is actually quite lovely but the stepsister is even uglier.

I've bicycled over Loveland Pass and Trail Ridge on a loaded touring bike and can't really say which one would be best. Loveland is steep but Trail Ridge will take your breath away...literally

Another alternative that I haven't mapped out would be to ride the TransAm to Breckenridge, then go over Loveland back to Denver (about 80 mostly downhill miles), the ride up and over Trail Ridge. That way you get to experience both.