For US travel Southwest and Frontier are very reasonable and bike friendly. Southwest is $50 with no charge for your other bag. Frontier, it depends on the type of ticket. With any but the cheapest class of ticket it is free. It is reasonable with their budget ticket. You need to keep the bike box under 50 pounds.

I think Southwest acquired Airtran so they now have the SW policy.

I usually use a box that bikes come in or a soft case if I will be flying to and from the same city. If I use the soft case I pad it well inside with cardboard.

Sometimes I Fedex or UPS my bike. I most often do that for the trip home. I have several times paid a bike shop to box and ship it for me. That has always been for the trip home when I didn't feel like dealing with boxing and shipping a bike in a strange city. The cost was always about $100, $40-60 for the shop and $40-60 for UPS.