How a bike is packed makes a significant difference in shipping costs.
All major carriers use "dimensional weight" using a formula (volume in inches / 166 =
#s ) that converts volume to a billable weight. There are also surcharges for specific dimensions, ie the longest dimension being over X, and more significantly, the second longest dimension being over Y, or the sum of all three dimensions being larger than Z.
These rules can hit bike shippers very hard. For example, both UPS and Fedex have steep surcharges if the second longest dimension exceeds 30" which is close to bike box size. So, two bike boxes, one being 60x31x8 and 60x29x8 can incur very different fees.
It pays to know the rules and pack accordingly, working around them to the greatest extent possible.
The best rates will be if the bike is packed with the front wheel, bar/stem, saddle and pedals off, and the fork turned backward, with the front wheel nestled against the frame, all in a flat box less than 30" high. In some cases even more money can be saved by packing in 2 smaller boxes, one from frame and stuff and the other for 2 wheels. The added cost for a 2nd box is more than offset by avoiding all the oversize surcharges.