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) 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 every one to two hours between 6 a.m. and 11 p.m., and costs $30 one way (with no savings on a round-trip ticket). 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 every two and a half hours between 9:30 a.m. and 7:30 p.m. (with an extra 10 p.m. departure on Sundays during the UW semester), and and costs $23 on-line or $30 from the bus driver. Get off the bus at the first Madison bus stop, which is UW Memorial Union right on the UW campus.