There are two ways to delete a ride from your account:
On your Bike:
Go to your profile by selecting your username in the bottom left-hand corner of the home screen and selecting "Profile". On the left, you will see a list of all your previous rides. Swipe to the left on the ride you wish to remove and then press "delete".
On your Peloton web profile:
To delete your ride online, log in to your Peloton account. Click into your profile and you will see a list of rides. Tap the 'X' in the top right-hand corner of the rides you would like to remove.