The bdb class or __init__ docstring needs to document the data members with a short explanation.  Some of the args need better explanation.  Some of this I may fill in *after* reviewing the proposed tests, when I understand the code better.  Reviewing pdb and IDLE's Idb and Debugger (my real interest here) will help.

is_skipped_module is public, by its name, but is not in the doc.

break_here: " If the breakpoint is a temporary one, this method deletes it."  maybe (if flag from effective is True)

The first comment and the code that follows do not seem to match.  IDLE does not set breakpoints for functions, so I cannot test the behavior here with its debugger.

set_break doc says filename should be canonic, but function then calls canonic.  So canonic not needed.  If it is, result is self.fncache[canonic_filename] = self.fncache[canonic_filename].  But I will leave suggestion as is for now.

get_stack: return 'size of the higher part': If higher part does not stop as self.botframe (which might be None?), the size is of the lower part.  I need to review frame and tb objects pin down this docstring.

I just pushed my changes.  Please review for typos and anything you think is a new error.  Otherwise, I think this is about good enough to merge.