Orio al Serio (BGY) is connected to Bergamo city centre by city bus number 1C, which stops at the Bergamo railway station, Porta Nuova, and continues up to the High Town (Città Alta). Tickets cost around €1.50 for a single journey, valid for 90 minutes on any urban bus. One standard suitcase is carried free. Service runs roughly 6am to midnight, every 30 minutes.
For Milan, Autostradale and other operators run coaches from outside the arrivals hall directly to Milan's central bus station. There's also a service to Brescia.