I ship plants bare root. I dig them up, rinse the soil off, wrap in moist paper towel and cover that with saran wrap. I mail in flat rate boxes so they reach the receiver in 2/3 days.

Something else to consider, especially during the hottest part of the summer, is how far across the country the plant will be traveling. That is why I haven't responded to some trade offers in the past, just to find out what their location was.
If not trading enough to make flat rate worth while, I prefer to trade with folks who are in mailing zones 1-4. Few folks give that a consideration though.

I think it always best too, to mail on a Mon or Tues, or else on a Sat, as the mail and packages do travel on Sunday.

According to link link below about Priority Mail...This service offers fast domestic delivery in 1, 2, or 3 business days1 based on where your package started and where itâÂÂs being sent.

Here is a link that might be useful: Priority Mail