One of two ways:
When someone sends you a message, you will receive an email which contains a ‘Reply’ button. Click on this button and sign in to reply. You cannot currently reply through your email client.
Log in and click on ‘Messages’ at the top right of your screen. Find the message in the list and reply through the app.
You will need to log in to BowerBird to reply to messages. If you need to confirm your account, you can do so here.