I fly Southwest and bring a bike enough times a year that I consider it "regular". This year, 2x roundtrips so far, probably one more in the fall. Last year, 3x. Year before, 4x.
Southwest charges $50 as noted above. Also, since you already have to check, you can check another bag free. I usually check 2 bags and they let me slide (2 free checked, $50 for the bike bag). Carry on just electronics in that case.
I've video taped various handlers with my soft case bag as they load or unload the plane - they are very careful with it, drop it about as hard as I'd drop it. I've carried two pairs of wheels (carbon faired plus alum), carbon only wheels, carbon/alum/combination frames, loaded it with various stuff (clothing, floor pump, helmets, tools).
I've been using this bike bag for a while, probably 10 years now. It's been very good so far.