I still don't think it's a fireable offense. It was a stupid thing to do. Maybe her so-called "pattern of behavior" put her in the should-be-fired category. Free speech may not be exactly what you want it to be, but we are free to flip someone off should we so choose.
Stop right there. You do NOT have freedom of speech while I am paying you to work for me. You are not free to discuss religion/politics/sex/racism at my place of business, period. That is my business POLICY. And while you are in my employ, you are most certainly not allow to flip-off anyone while driving the company bus.
Free speech is about GOVERNMENT attempting to limit what you can say. It is NOT about what, I as your employer, state you can and cannot say or do while in my (or for example, the local school systems) employment.
Let approach this a different way. Since you believe flipping the bird in front of children is not a firable offense. How about is the bus driver said outloud "F%^$ that George Bush" or "F^%^ that congressman"? that must be allowed under free speech by your argument. How about if the bus driver dropped the N-bomb along with the F-bomb?
I'll go you one better. In the NFL, you can and will be fined/suspended for behaviors/actions that you do entirely OUTSIDE your work obligations and outside of your required working hours. When you sign a contract to work for any employer, you almost always agree to act in an ethical, professional and moral manner.
And I am free not to employ your sorry a$$ if you do so while working for my company.