The only practical transportation from Madison's Dane County Airport to campus is by taxi, which costs about $20 one way to the UW campus. (The city bus requires a change of buses on the way to campus.)
From Chicago O'Hare, take the Van Galder Bus (phone 1-800-747-7407) from the (international) Terminal 5 (lower level, gate 5E, leaves 20 minutes earlier) and from the Bus/Shuttle Center (in the main parking garage on the street level between terminals 1, 2 and 3). The ride takes about three hours, departs daily rouhgly every hour between 6 a.m. and 12:30 a.m., and costs $30 one way (if ordered on line). Get off the bus at the last bus stop, which is UW Memorial Union right on the UW campus.
From Milwaukee airport, catch the Badger Bus (phone 1-877-292-8259) outside the baggage claim area (lower level, south end of airport). The ride takes about two hours, departs daily roughly every two and a half hours between 6:15 a.m. and 9:05 p.m., and and costs $23 on line or $30 from the bus driver. Get off the bus at the Madison bus stop, which is UW Memorial Union right on the UW campus.