Not if your fare includes a checked bag on some routes: US to Europe: Free. Within the US: $45 per bike, each way.
How much does Alaska charge for a bike between the US and Europe?
Free (counts as a checked bag). Included in your free checked bag allowance. No overweight fee for bikes up to 70 lb.
How much does Alaska charge for a bike within the US?
$45 per bike, each way. Counts as one of your checked bags. No extra bike fee. Main and Saver fares within the US don't include a free checked bag. First bag: $45 ($30 within Hawaii).