Hmm... When I think of bicycle trekking somehow an image of "Extreme Touring" comes to mind. That is, going to remote destinations domestically but most likely international. Long sections will be done off-road under uncertain conditions (road, weather, etc.) You will have to walk your bike in certain sections where the road becomes singletrack, rocky, etc. You might be isolated for a few days, so you absolutely need to be prepared with gear and provisions. Places in the world where "bicycle trekking" comes to mind: Alaska, Southern Utah, Bolivia, Patagonia, Nepal, Tibet, "Stan" countries. Bike trekkers prefer Mountain Bike geometry and butterfly handlebars to maintain control of their bikes over this extreme terrain.