Not during the 7 days. But the trial does need a payment method to start, and it becomes a paid subscription when it ends unless you cancel first. Here's the detail.
When you are and aren't charged
The 7-day trial is free, and you pay nothing during those 7 days. You do need a payment method on file to start it, because the trial runs through your store (the App Store on iPhone, or Google Play on Android). When the 7 days are up, it turns into a paid yearly Bend Premium subscription and you are charged the yearly price, unless you cancel before then.
The free trial is a one-time offer
You get the trial once. If you have already used it, starting a membership charges you right away instead of beginning a new trial. Whether you qualify for the trial is decided by your app store, not by Bend.
If you subscribe
Bend Premium is the paid subscription, handled by the App Store on iPhone, or the Play Store on Android. Starting the trial signs you up, and the paid period begins automatically once the trial ends. You can cancel anytime through the store you used, and if you cancel before the trial is over you will not be charged.