What you need to do is simply change the default avatar that your site uses (which bbPress also uses).
Check this out http://www.wpbeginner.com/wp-tutorials/how-to-change-the-default-gravatar-on-wordpress/
I have been trying for a while to add custom avatar in my local hosts sites without using plugins. I have been following the reference @jaredatch listed as well from codex How to Use Gravatars in WordPress and many other similar articles.
I get the Avatar logo name displayed under Default avatar but logo does not get displayed. I followed the direction for my image location (under images folder in my theme, together with pther folders inc, layout, js etc). Yesterday I spent my entire day to troubleshoot but I can’t solve this problem. Any help will be greatly appreciated.
I don’t follow. This topic is about setting a default avatar – is that what you are trying to do?
If so, please see http://www.wpbeginner.com/wp-tutorials/how-to-change-the-default-gravatar-on-wordpress/
If the text is showing up, but not the image, the image path is incorrect or the image doesn’t have the correct permissions.
You should be able to define the path using the function, as outlined in that article.