Bi-di text is supposed to just plain work. AIUI, bdo is a kludge for when your data is backward, and if necessary, these characters:

‬POP DIRECTIONAL FORMATTING
‭LEFT-TO-RIGHT OVERRIDE
‮RIGHT-TO-LEFT OVERRIDE
[download]

can be used instead.

Test:
Normal: My name is יצחק בן אברהם, but I'm not the famous gentleman of that name.
Reversed w/ override: My name is ‭םהרבא ןב קחצי‬, but I'm not the famous gentleman of that name.