Can keywords made in Bridge and/or Lightroom be seen by any other program?

First of all keywords are written to image files as plain text, tagged in XML format. So yes, lots of apps can read them. HOWEVER...

Metadata is organized in "namespaces" which designates where and how data is stored in a file. Keywords can be written to as many as five namespaces and image apps may or may not read all of those.

Hierarchical keywords are simply text with a delimiter (for example, "bird|raptor|hawk"). Reading and writing and recognizing hierarchical keywords is up to a specific app. In Bridge, you can actually choose how to handle these cases. So you'll want to check the documentation for your app to see how it works.