The bikes found their way through a Heathrow transfer to Schiphol, where we wheeled them out of their boxes (in fine shape), re-assembled them, and rode off into Amsterdam, a great way to attack jet-lag. A woman at an airport info counter gave us a brochure, "Naar Schiphol op de fiets" ("to Schiphol on bike"), whose text is all in Nederlands, but has a terrific map on its back. Even this sensible tool was unnecessary, as the Dutch have placed plenty of bike-oriented direction signs (white with red text) at nearly all the critical points along the way, and we arrived at our Jordaan district hotel in fine condition.
We then proceeded to have three weeks of rain-free Dutch spring biking, from Amsterdam down to Rotterdam, back to Amsterdam for Queen's Day, and then up to Texel and Leeuwarden. After returning to Amsterdam by train, we loafed a couple of days, and at last made our way back to Schiphol to catch our flight back to California. We went through the same minor knock-down of the bikes, though this time United charged us 30 guilders ($18) for the 2 boxes, and a bomb-sniffing dog was brought in to inspect the boxed bikes. Sadly, this time we had to travel in the "cheap seats", but when we claimed our bikes at SFO, all was still well (the boxes were a bit scuffed up, but the bikes came through fine).
By the way, the Dutch railway (NS) allow bikes aboard any train, charging a small extra fee for the bike. Be sure, if at all possible, to buy your tickets at a station, since there's a bit of a surcharge when the conductor processes your fare aboard the train itself. Theoretically, with a bike you're supposed to board the last car of a train (marked with a little bike symbol), though we've had conductors gesture us onto other segments. Best to ask an NS person on the platform what to do (where to be standing), while waiting for the train to come into the station.
So, to pull this tale together, you could take your bike from Amsterdam to Schiphol by train pretty hassle-free, or you could just ride there. Either way, the airline probably has boxes for you to use (call ahead), and it really is easier rolling a bike around than dragging it in a box.
If you decide to pedal to the airport (about 14 kilometers), the route is approximately this: find your way to the Vondelpark and ride its length, exiting at the main west gate. Cross the street and continue straight (Bockstraat?) for about eight intersections, until you must turn (water); go left/south a few intersections until you reach Heemstedestraat. Turn right/west and follow Heemstedestraat (it becomes Plesmanlaan, I think) through Slotervaart and Sloten (look for signs for Badhoevedorp and Schiphol-Centrum). Pretty quickly you'll be seeing planes and airport-related stuff, and signs will show you the rest of the way. It's really gratifyingly simple, but for good order you can probably get the Schiphol map-brochure at some fietswinkel or other in Amsterdam.