What membership is this? Your account is supposed to be free already once you've gotten CSP. What are you paying for?
There is the Gold membership, but that's mostly for getting clippy points to get paid assets. There's also the option to buy gold for assets, but that's another optional choice. When you go on to the store, most of it is free assets. So you don't really need the gold membership (it's just nice to have IF you want certain paid assets).
And you find the shop from your CSP launcher or by going to the URL. Long as you have the account, you have access:
Are you using a PC desktop or an IPad? If it's an IPad, then yeah -- there is that subscrption for $10 a month. But if it's a PC desktop, it should be the one payment, and then it's optional to pay for assets or that gold membership. You shouldn't have to pay to use the asset shop if you're not trying to get paid assets.