I biked that route in reverse 9 years ago. Absolutely beautiful. It involves 3 ferry rides across 3 different lakes. Hopefully, the tourist ferry boats are still running. Ask around in Bariloche. A tourist office or tourist agency should be able to tell you.
You can view a good map at:
From Bariloche, bike west to Llao Llao, about 27 km. Take the ferry across the lake to Puerto Blest. From there, you bike on an unpaved level road about 3 km to Puerto Alegre, where you catch another ferry across the small Lago Frias (which I believe was shown in the current film, "The Motorcycle Diaries"). Argentina has a small customs/immigration office along the lake. The Chilean counterpart is on the other side of the pass you must cross.
Now comes the hard part, though it's not that long. You have about a 4km very steep unpaved (9 years ago, at least) climb up Paso Perez Rosales, 1022m, which is also the border with Chile. From there, you will have a drop down to a valley, then a lovely level ride to Peulla. All of what I have described can be done in 1 day. At least, I did it in reverse in one day (from Peulla, Chile, to Bariloche, Argentina). You need to find out what time the ferry departs Llao Llao, assuming the ferry still exists, and time your departure from Bariloche accordingly.
In Peulla, there were just 2 places to stay 9 years ago. There is an expensive hotel. But there was also an unofficial hospedaje. A very nice man rented out 2 rooms at a very cheap price (about US$10 when I was there) which included a good dinner and breakfast. If you're lucky, that option will still be available.
From Peulla, you take a ferry across Lago Todos Los Santos. The scenery during the boat ride is simply magnificent. There are a lot of pretty lakes in "la region de los lagos", but that lake was easily the most beautiful. As you approach the western end, you'll see the impressive Osorno volcano.
One of the great things about this route is that there is no traffic all day, except for perhaps a bus which might pass you. There is no way for a car to get to these roads, because the ferry boats only take foot passengers and cyclists.
When you get off the boat at the western end of the lake in Petrohue, there's a downhill and there will be traffic again. After a few km there are the pretty waterfalls (Salto del Petrohue), and the pavement should begin again. From there, it's an easy ride along huge Lago Llanquihue toward Puerto Montt. I think I stayed in a hospedaje along the lake, so I could get an early start to reach Petrohue and the boat. You won't have to worry about that going in the other direction.
I hope the ferry boats are still operating, because it's one of the prettiest regions I've ever seen by bike, and it's a delight having no traffic at all.