I don't know the situation you are describing because it never happened to me.
If you are actively trying to complete bounties, chances are you are trying to optimize your routes and group them together. When the public event one drops, I group it with 100 kills / 10 fallen leaders / 6 patrols on the cosmodrome / 30 melee kills / etc., and hit the cosmodrome right before the divide one or the skywatch one begins.
With all the going back and forth between those two areas, I usually have just the right amount of time to complete or nearly complete the other bounties, while doing my 3 public events.
The public event feature is designed so that you are supposed to see them randomly. And rarely.
And for the hardcore players, there is a way to chase them down.
Sure it's not perfect, but it's working quite well, for what it was designed to be, and for us bounty runners. ^^