To get to the bus, head towards the FLYCAR stop 22, in Malpensa Arrivals Terminal 1. Price is about 20 Swiss Francs (Note 15. April - they take Italian Lira).
The Airpullman stop is stop 19 in Terminal 1. Price is 30 Swiss francs and stops at Chiasso (not Mendrisio).
In Lugano you will end up at the FFS - Federal Railways of Switzerland station, where you have connections to bus line "9" in Lugano (courtesy of Azienda Trasporti della Città di Lugano - sorry no website for them), as well as the FLP train to Ponte Tresa (not part of FFS), and a funicular cable car to the central part of Lugano.
In May I should have some more to write about the actual experience, so please stay tuned. For those of you who have already rode this bus, please feel free to give me (firstname.lastname@example.org) an email about your experience.
You can also use AIR PULLMAN BUS EXPRESS, stop 19.
In a fear that Air pullman bus express will accept only Swiss Francs for payment instead of Italian Lira (which doesn't make a lot of sense since they're departing from Milan Malpensa in Italy [???]), I have decided to change some money at Thomas Cook in the Stanford Mall (near Stanford University in Palo Alto, California).
I changed $51 into 80 Swiss francs (plus a $5 fee). From this I received two 20 franc notes and the rest in 10's. (The 20 Franc notes had Arthur Honegger and the 10 Franc notes had "Le Corbusier" - to see the notes, please go to Swiss National Bank.
Only 11 days until I leave for Milan via Washington Dulles.
But transport from Lugano to Mendrisio as well as Chiasso (and viceversa) are not permitted, only transit to Milan Malpensa.