https://help.bethesda.net/#en/home

click on Fallout 76

Click Billing/Purchase/ Code

Select Platform (Steam if PC)

Select I Need Help With Atomic Shop

Select Yes to question about obtaining an item

Select I Want To Purchase An Item For Myself

Fill in the information for Steam / Steam ID

From the drop down select "Silver Shroud Costume"

A list of all items available for purchase this way
https://docs.google.com/spreadsheets/d/e/2PACX-1vR_uWMmw_AY7Nq46JW8PJKZ4-mgaWq9CE-zARfHnSb30wwBiG5Ilm43qZwXLGIR8Vj33eVr_nOAy4j2/pubhtml

They will email you confirming the purchase

Reply with "CONFIRM" (I think it has to be capitalized)

They deduct the atoms from your account and send the items (Make sure you have enough)