Below is what the SW website says. Bikes fly free if they are under the size and weight limits. The first time I flew SW with a bike I was inexperienced and they told me to wheel the bike around the back instead of putting it on the scale to be weighed. I thought they had a larger scale in the back they wanted to use but when I got it to the back they said that it was a bike and there was a $100 charge. I knew that wasn't right because I had read that any oversized bags was $75 (and though that if I was under the limits there might not be a charge, but didn't really know). I called them out on the $100 and they backed down quickly to the $75 charge for oversized baggage that I quoted from their website. They never weighed the bag though and I know for a fact that it was well under the limit.
When I got to where I was going I found that I was the only person on the team that got charged for a bike. Going back I put that bike right up on the scale and they saw it was under the limit for size and weight and checked it no problem. SW has the no hidden fees motto. Hold them to it because I guaranty that most of their employees don't know the ins and outs of all special items they have listed on the page I copied the below information from and I can guarantee that most of them don't know that a soft bag with a race bike it is is going to be way under the weight limited where hard case, mountain bike, etc. won't be. So make them weight in and verify the size or they will just assume what ever the last guy checked is the same thing you are checking.
Know what the size weight limits are and what the charges are and you will get through no trouble. If you don't know the limits and charges they are going to make you pay extra for anything that doesn't look standard to them.
Sports Equipment - Baggage Allowance Any of the items listed below may be checked in substitution of one piece of the
free Checked Baggage allowance for each Passenger at no charge on a one-item-for-one-bag basis. If the item of sporting equipment exceeds 50 pounds in weight or 62 inches in size (outside length plus height plus width), excess weight and size charges may apply.
- Bicycles (defined as nonmotorized and having a single seat), including Bike Friday and Co-Pilot, properly packed in a hard-sided bicycle box that fall within the dimensions and weight limits established for normal Checked Baggage, (i.e., 62 inches or less in overall dimensions and less than 50 pounds in weight). Pedals and handlebars must be removed and packaged in protective materials so as not to be damaged by or cause damage to other Baggage. Bicycles packaged in cardboard or soft sided cases will be transported as limited release items.
Note: See below for information regarding bicycles that exceed our checked baggage size limits. Additional charges may apply.