This help page should address your need for product bundles:
After the buyer finishes checkout, and once the payment processor notifies us they have completed the buyer's payment, we grant the buyer access to a thank-you page we automatically generate for their transaction, where we would present their unique download link(s). We also send the buyer a thank-you email message with a link to reach their thank-you/download page in case they did not proceed there after checkout. Every download link we issue expires after the number of Attempts or Hours (whichever comes first) that you specify in each product's settings.
Is "one-time payment access to a membership site" you mention related to those download-bundle products somehow, or was that meant to be a separate question?