As good fortune would have it, Iberia (0171-830 0011) has a special of pounds 123 return, including taxes, for its evening flight from Heathrow. So even with tube fares to the airport, you'll be spending less than pounds 130 on getting there.
Bilbao airport is still friendly and low-key for a city that is shaping up as a hot metropolis (smart expansion is imminent). It has a helpful tourism desk offering a map of the city and a free local listings magazine.
A good central billet is the Carlton (00 94 416 2200), recently renovated to enhance its 1920s opulence, with a cut-price weekend rate of 13,500 ptas (pounds 56) for a single or double room. It has a hushed oak-lined dining room with an excellent menu of the day at pounds 12.50 (but limited choice on Sundays). A more modest alternative is the friendly and elegant Iturriena, (00 94 416 1500) which charges 5,000 ptas (pounds 20) for a single room, 6,500 (pounds 26) for a double in the old quarter, the casco viejo. It's a bit noisy on Saturday night as it's in the thick of roaring bars, but you won't mind that if you're in one.
I usually end up buying shoes in Bilbao, more elegant and cheaper even than in Madrid. Designer clothes, sunglasses and handbags are unflashy and unencumbered by gilded chunks, and good value with nearly 250 pesetas to your pound. Bilbao is renowned for its austere chic, perhaps the only Spanish city apart from Barcelona, where less - make-up-wise and shoulderpad- wise - is more. A relief, in a nation of over-decorated females. But ration yourself: you haven't come to buy (unless, perhaps, a bottle of Basque firewater at the airport) but to absorb spiritual and physical nourishment.
Eating (after visiting the Guggy) is the real purpose of your visit. Bilbao is gastronomic heaven. Basque cooking combines subtlety and imagination with the finest of raw materials, for which read mainly fish. The Basques, who discovered cod off Newfoundland in the early 16th century, have refined centuries of fishy lore to the point of self-indulgent perfection. Tapas (called pinchos) attain undreamed-of richness, variety and irresistible gobbleability. Rosy shredded crab, anchovies soaked in wine vinegar and garlic, hake cheeks (yes) draped with a succulent sliver of marinaded red pepper. Just head for those groaning zinc counters and point.
Pastries, cakes, late afternoon coffee or hot chocolate are good comfort fuel, should a damp, chilly wind sweep up the estuary from the Bay of Biscay.
Antxokia (San Vicente 2) is a Basque cultural centre-cum-bar and night club where you can eat a spicy fish stew or lentils with fierce garlic sausage at lunch time and, in the evening, knock back squat tumblers of txacoli, the tart young local wine, to the haunting sounds of local musicians who sound like the wind in the trees.
Live concerts heave with hectic, tight-packed, non-aggressive excitement, and Bilbao is plugged into the international music circuit, with a sophisticated taste ranging from the Levellers to Radiohead.
Bar-crawl in the old quarter, recently renovated and just this side of film-set cute, a pedestrian area of crisscrossing little streets to wander and lose yourself. Many bars sport the red-white-and-green "ikurrina", the Basque nationalist flag. You may find English elicits a friendlier response than Spanish, which some consider the language of the oppressor. Bilbainos revere Brits as the founders of their football club, Athletic, whose idols are pinned up everywhere. No need to worry about closing time: the place will be jumping long after you fade.