Adventure Advisor Answer: 
It just so happens that Spain is among the most fat-tire friendly countries in the world, boasting an endless network of trails with varied terrain, comparable to our Sierra Nevadas (which, by the way, were named after the range in southern Spain). Accordingly, finding an outfitter in Granada is just about as easy as finding one in, say, Durango. But if you’d rather book a tour from home, here are a few suggestions:

• For quick tips and tall tales, contact Sal Lilienthal, director of The Bicycle Tour Company International. Though his company offers road bike tours, not mountain bike tours, Lilienthal has lived on the Costa Blanca and mountain biked all over the country. He’s got info aplenty about Spain’s mountains, which he’d be happy to share on request. Phone: 888-711-KENT.
• CANFAB, a British company that specializes in outdoor excursions, offers mountain biking tours in the Picos de Europa near the north coast. Scenery ranges from ancient forests to limestone cliffs to wildflower-dotted meadows.
• Andalucia Center for International Tourism has a mountain biking brochure that details 120 routes in southern Spain. They can also recommend local outfitters. Send requests to: C.I.N.T.A., Ctra. Nacional 340, Km 189.6, 29600 Marbella (Malaga), Espana.
• Espana Bike Travel runs mountain bike trips in Spain’s Canary Islands—a bit of a trek from Spain proper, but worth the journey. Groups are arranged according to ability level, from pavement peddlers to hard-core “extreme” cyclists.