bbPress.org

Apologies for the delay is responding to this.

Assuming you are ok with FTP, then

find
wp-content/plugins/bbpress/templates/default/bbpress/form-anonymous.php

transfer this to your pc and edit to remove

<p>
			<label for="bbp_anonymous_email"><?php esc_html_e( 'Mail (will not be published) (required):', 'bbpress' ); ?></label><br />
			<input type="text" id="bbp_anonymous_email"   value="<?php bbp_author_email(); ?>" size="40" maxlength="100" name="bbp_anonymous_email" />
		</p>

		<p>
			<label for="bbp_anonymous_website"><?php esc_html_e( 'Website:', 'bbpress' ); ?></label><br />
			<input type="text" id="bbp_anonymous_website" value="<?php bbp_author_url(); ?>" size="40" maxlength="200" name="bbp_anonymous_website" />
		</p>

and save

create a directory on your theme called ‘bbpress’
ie wp-content/themes/%your-theme-name%/bbpress

where %your-theme-name% is the name of your theme

Then transfer the file you saved above and put in in the directory called bbpress that you created above, so you end up with
wp-content/themes/%your-theme-name%/bbpress/form-anonymous.php

bbPress will now use this template instead of the original

Alternately if this all confuses you, I can do this as a plugin, but it would be a paid bit of work (but not expensive) – contact me via http://www.rewweb.co.uk/contact-me/