I have a business that basically works using a subscription (I'm simplifying here). I see that Stripe accepts Bitcoin, but it's for a one time payment. Is there any way to save a customer's Bitcoin info, or is it just for one time payments? The nice thing about a credit card is you can keep charging it...
Bitcoin transactions are "pushed" by the payer. There is no way for the recipient to "pull" payments.
You should use a new address for each customer. That way you can see who paid their subscription fee by checking which address received the payment. However, the customer would still have to repeat the payment every time.