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. ^^
Yep. I clump all my bounties together. The problem is most bounties are done within a single PE window. They don't take long.
Then, as mentioned, if you have no other reason to be in patrol areas you're left with 2 more PEs to complete and nothing else to do while you wait.
The problem here that I find is that PEs have not been reliable for me, even the tank one hasn't shown up on occasion. This means I need to dart around hoiping the next one will spawn correctly.
Did this yesterday. Tank didnt' spawn and there was one in Rocket yard in a few minutes. Biked there and it was a kill mission. Got the enemy down to low health by the second checkpoint, then he just disappered and the event ended (2 more checkpoints to go).
Then there was one due on Forgotten Shore. I biked there with 3 minutes to spare. Waited. Didn't show. Waited 10 minutes past the timer. Didn't show.
They're fine being random events that spawn /if/ you have reason to be patroling. As soon as you don't have any reason (not more bounties, no materials you require, etc..) they can be a little bit frustrating if they don't spawn.