You need a separate subscription for both Pokemon Home and Pokemon Bank.
You may already have Pokemon Bank, but in case you don't, to download it you have to pay a $4.99 annual (1 year) subscription fee (in the U.S.A.).
As for Pokemon Home, you can download it for free. To be able to transfer Pokemon from Bank to Home, however, you need a premium subscription for Pokemon Home. Nintendo offers three different payment options for premium subscriptions:
-- $2.99 for premium for 1 month
-- $4.99 for premium for 3 months
-- $15.99 for premium for 1 year
All of these are offered if you live in the U.S.A. If not, you can find the payment information for your country on your Nintendo eshop.
Sources: Nintendo Switch eshop and Nintendo 3DS eshop
Hope this answers your question!