There is a huge jump and price once the volume goes above a certain total. Using the BIkeflights estimator I found the various limits on a traditional bike box (rear wheel on, seat, bars and front wheel removed) where shipping from Oregon to Seattle stayed under $60 rather than $160+.

54 x 8 x 30
54 x 9 x 28
56 x 9 x 28
55 x 8 x 29
52 x 9 x 30

Go over any one of those dimensions with and the price jumps $100. Of course, I ride smaller bikes so it is easier to cram my size into these boxes, but medium size bikes are fine.