How do I tell python to ignore a certain specified bone when it is not present in the armature

You can use try statement in Python script. See the document here.

A simple script:

a_list = [1,0,2,3,4,5]
result_list = []
while a_list:
    try: # Try to run this block
        divider = a_list[-1]
        result = 60 / divider
        result_list.append(result)
    except: # if "any" Error happen, do this block
        print(f"Oops, something go wrong: divider:{divider}")
        break
    finally: # whether there is an error or what, run this block
        a_list.pop()
result_list

Output:

Oops, something go wrong: divider:0
[12.0, 15.0, 20.0, 30.0]

Please don't silently bypass an error in code, let user know what happens and if possible, let them decide what to do explicit.