hmmm the bosses are not really thinking this through. Nobody should go around the woman's house and apologies and certainly not on their own. A bunch of flowers and a card is perfectly acceptable, but really you shouldn't start giving beyond that without it being in full settlement of the claim.
Obviously you are aware that the purpose of coning off the walkway is mainly to ensure anything you drop doesn't kill or injure someone.
make sure you limit your dialogue to an apology and at no point discuss what you should and should not have done. if she argues.. stick with the apology.
"again I am sorry for the distress and inconvenience.". etc.
may be worth having your phone on record in your pocket.