Several agencies rent out mountain bikes (5$ a day or $1.25 a hour).
But make sure that you or someone with experience checks out the bikes and ensures that they are safe to use. Especially check if the gear is clean and oiled enough - bikes look really good, but are sometimes not maintained like they should be.
Also be sure to understand who has to pay for damage to the bike should it occur.
A popular ride is the 61 kilometre, mostly downhill, to Puyo. The first 18 km to Rio Verde is strewn with impressive waterfalls, some reached by mini cable cars across the valley.
Rio Verde's Pailón del Diablo is the most dramatic.
The frequent tunnels on this road mostly have bike bypassses and the only one you need to go trough is the first one. There are good signs indicating where to go all the way to Puyo.
From Rio Verde or Puyo there are frequent buses back to Baños, some of which will put you bike on the roof. It is also fairly easy to hitchhike your way back on a pick-up truck.
You can also sometimes include a small bungee-style jump off a bridge some 30 minutes from Baños.
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Based on a work at Wikitravel.org & Traveldudes.org.