Hard Bounces can be bulk deleted from the BOUNCED tab in your messaging report.

After a message send is completed you can delete any hard bounces from the BOUN CED tab by clicking the Delete Hard Bounces link.

Soft bounces are not removed as they are potentially not a permanent failure.

Do I have to pay for messages that are bounced?

We are charged by our telecommunications partners for the attempt to deliver the message not the delivery itself. This is why we must charge for the send to the carrier. 

To limit the amount of bounced messages you are paying for, you can either do HLR cleaning of your list or you can make sure you are deleting hard bounces after messages are sent.