Scandinavian Airlines has round-trip flights from Chicago (ORD) to Bologna (BLQ) for $478-$514 with a connection. Flights September, October, November, December, February, and March. Extended weekends available.
A carry-on bag is allowed without fee. To upgrade to a checked-bag fare, it’s about $38 each-way. Carry-on bag must be 18-lbs (55x40x23 cm) or less.