After stopping for lunch in Santa Gertrudis, an attractive village with several good bars and restaurants, I reached Es Broll de Buscastell. This isolated valley, famed for its spring, is where I encountered the wall.
Resting my bike on the ground, I went to refill my water bottle from the valley's artesian well. As I drank, a fairy-like tinkling sound drifted across the valley: goat bells.
A four- or five-strong herd sauntered into view. Then, from out of the trees, a small wizen-faced man in short trousers and natty grey cap appeared.
He smiled and motioned for me to lift my bike up to him and deftly he lifted it onto the path above.
The following day I headed north to Sant Joan de Labritja, the least populated part of the island. Here farmers work the land much as their ancestors did.
Some farmhouses and rural estates have been converted into luxurious hotels and form part of the agrotourism movement, based upon respect for the island's environment and heritage.
Casa Vilda Marge, a 400-year-old country house, is one such property and Fabian Puig, a slim, sociable man who runs this peaceful hotel with his wife Claire, is keen to keep the tradition alive.
Breakfast comes with a medley of fruits from the estate: Kaki, grapes, fig and melon.
Helping myself to more homemade jam one morning, I asked Fabian what beaches and coves he recommended. "S'Illot is very nice," he replied. "Only 10 minutes by bike."
I soon found myself whizzing down an empty stretch of road but somehow I ended up at Cala Xarraca rather than S'Illot des Rencli. No matter, I thought.
Cala Xarraca is still rather lovely, a small bay with a restaurant on the left and several fishermen's houses piled upon the rocks to right.
The road back was long and steep and as I puffed my way uphill I recalled a conversation with Fabian: "One time, in Costa Brava, I was driving up a mountain and in the mirror I see two cyclists: Lance Armstrong and Tyler Hamilton. I am in second gear and they go straight past me."
I resort to walking the final stretch uphill then freewheel my way toward Sant Joan, a quiet, pristine village untouched by tourism.
As the sun set on my final evening I went looking for S'Illot again. The low purr of farm machinery and chattering birdsong hardly troubled the stillness of the air.
I concentrated on my front wheel, crunching over dusty stones and swerving around plate-sized potholes, racing against the light.
I don't know if it was S'Illot I found or my own snug harbour but I can think of no finer spot from which to watch the sun go down.
Details
THE FLIGHT Ryanair flies from Stansted to Ibiza, return fares from £8. www.ryanair.com
THE HOTELS Hotel Sa Talaia has doubles from £90 B&B, www.hotelsatalaia.com. Casa Vilda Marge has doubles from £60 B&B, www.casavildamarge.com.
THE BIKE HIRE Ibiza Sport rents mountain bikes from £15 per day, www.ibizasport.com. You can download cycling routes at www.ibiza.travel/en/mapa_rutas.php www.spain.info
