UPS is the best way (if they require what is in them, "yeast samples". Enclose each bottle in a ziploc plastic bag, then wrap it with bubble wrap and tape it. After each bottle is plastic bagged, bubble wrapped, and taped, put a garbage bag in a box and fill it with those white thingys

to where your packed bottles can't be shaken or rattle!

Secure the garbage bag, tape the box and you are ready.
This is probable overkill, but I want to make sure my entries arrive intact for the winning selection.
Good luck!