Upvote:1
99%, the rules for bicycles are for your regular, non-folding bicycle. Folding bicycles, despite their recent popularity, are an edge case they haven't considered yet.
As for the case, there shouldn't be anything preventing you from checking it as an over sized item, for which you would have to pay. However...I, me, personally, would not check the bike in a soft case, even if you tag it as Fragile.
There are hard shell cases for folding bikes. Note, I do fully understand the dilemma of transporting a bike, then being stuck with a hard case. :(