Cycling independently takes a certain pioneering spirit and a greater tolerance for discomfort. It’s up to you to rent or bring your own equipment and to arrange food and accommodation; if starting from Kathmandu, you’ll need to organize transport out of the city or else put up with some ugly traffic. You’ll definitely make mistakes finding your own way, which might mean spending more time than you’d intended, getting lost or having to backtrack, or spending more time on trafficky paved roads and less time on trails. However, you’ll have more direct contact with local people than you would with a group.
Day-trips in the Kathmandu and Pokhara valleys are the easiest to do on your own, since you can rent bikes in both cities. Though you probably won’t find the more obscure trails, you’ll no doubt stumble upon others. If you’re riding long-distance without vehicle support, you’ll have to tote your own gear and may find yourself spending nights in primitive lodges where little English is spoken. This will be par for the course if you’re on a long tour of the subcontinent, though, and the going is certainly easier in Nepal than in India: the roads, for the most part, are less busy, and there’s less staring, hassling and risk of theft.