Thanks @joshuaabenazer! The caption is now visible in the rtMedia edit page in BuddyPress, but it is read only and shows up as text. I am not able to edit it.
It is showing the caption for the image that was added in the WP Media Library>Edit Media. But when I update something like the title of the image in the rtMedia edit page in BuddyPress, the caption is removed. I am guessing because there is not a field for input, so it thinks it is blank and then overwrites the caption that was there. ??
Is there a way to change it so that it can be edited? Thank you, again, for your time!
Edited to update: It works perfectly!!! I had copied the code that was in the email sent from this thread, and it did not quite work, but the code that is here now (above) works perfectly! Including linking, saving, displaying properly. Everything! Thank you so much!! This is a great feature to have the caption field!