I have been an Ebay member for a few years and an avid collector of  bobbleheads, cards and other sports memorablia.  On the subject of shipping - there is nothing worse than opening that long anticipated box with - a broken bobblehead inside!  Despite the wasted time effort and money, broken bobbleheads and figurines, etc. are basically worthless.
 I always pack styrofoam peanuts,  plastic bags or bubblewrap in the bobblehead case or box to first secure the piece from moving.  Then, I pack the small box inside a shipping box, which is also securely cushioned with styrofoam, newspaper, plastic bags and/or bubblewrap. ** Shipping boxes are easy to come by and can be delivered to your house free of charge through Ebay or the USPS website.  The USPS website will also send  free labels and stickers**.  The box is then securely taped with packing tape.  A little shake will tell you whether or not your package is secure.
 It is NEVER a good idea to ship a breakable object inside an envelope.  Double boxing is the only method that should be used with fragile items.  Thank you.