The icons for adobe are usually kept very simple. The one for "Adobe Bridge" just has the a capital letter B and a lower case r. Its the abbreviated version of the word. The adobe part is not represented in the logo because all adobe icons have a simple unique style that is consistent in the icons of the other programs.
This is a Adobe Bridge icon. It is available in PNG and vector. Downloading is free for PNGs up to 100x100px.