To use your existing Bridge wallet with a different email address:
Open Bridge and click your email at the top.
Click 'Change email address'.
Provide the email you'd like to use, then click 'Change email address'.
Open the inbox for the email address you provided. When you receive an email from Bridge, click 'Verify new email'.
Open the inbox for your old email address. When you receive an email from Bridge, click 'Confirm change'.