> How do you buy bitcoin and have it go directly into a cold-storage wallet in one transaction? 

That's not a good idea which is why it's not easy to do.

Mostly because of trust issues and it's more vulnerable to intercepts like man in the middle attacks.

It's super easy to replace a Bitcoin address you copy to your clipboard with another address belonging to someone else. 

For your own security, do the transfers to cold storage yourself. Fees are very cheap at the moment so, now is the time to learn.  Do a few transfers of tiny amounts of Bitcoin to cold storage until you become comfortable with how to do it safety. A couple of dollars spent now on Bitcoin fees for peace of mind is a bargain.  

 I didn't think about it that way. Thank you. That's good advice and a better way to approach it.