For my trad bows its a soft case but for my compound its a hard case. Im a traveling hunter so my case has to protect my gear on flights or if its mailed, the rough handling of carriers or in the back of my truck or a trailer. I have a plain Jane Plano that I ripped all the foam out of and customized to fit my exact needs. You dont have to spend big dollars, just get a reasonably priced case and re-foam it . you can spend very little but end up with a fantastic, customized hard case.
I started with this.
And did this. When I fly or ship or drive to remote trips I pack some camo gear in the case as well to further pad my gear. You need camo shirts and even socks and briefs so use them as additional padding. (padding the bow with week old underwear and socks keeps TSA folks from spending a lot of time rifling through your gear)
Even if you dont plan to fly now, make a case capable of this level of protection just because your gear is worth it and it can be done at low cost.