We picked a couple figs, and there were ants on them, and maybe some other really tiny bugs inside one, but not sure.  Days later, we picked some more and they seemed ok - no sign of bugs.  Today I picked a couple more, and I could see ants crawling on the tree.  I see a lot of articles about how to get rid of the ants, so we can try those remedies, but my real question is - are these figs safe to eat, if we don't see any bugs on the ones we pick?

Ants won't kill you.  Cut the fig in half before eating and look for rot (caused by bugs) and eat if none exists.

And the solution to the ant problem is Tree Tanglefoot:

http://contech-inc.com/products/treetanglefoot/

I had put a 20 gallon container on a tree stump in my back yard not knowing there was an ant nest there, one day I was checking the roots of it and all of the sudden I saw a ton of ants and eggs inside the pot.  I moved the pot and they disappeared, I also had 4 figs ripening on it and the ants didn't do anything to them while  they were there, I was surprised. I have since put diatamaceous earth on the ant hill and they seem to have gone down in numbers.

Judy
I just came across this easy to apply method for ants control. I hope it works :

Lots of ideas from the videos above especially the 2nd one.  Just curious if anyone would swear by any of those?

Well, I am gonna give the Boric acid and corn syrup traps a try. Set them out this evening. Used empty soda cans with a flap cut open on the side instead for easy filling/refilling and protection from elements and pets. We'll see...

Tanglefoot around the base of your tree will prevent them from climbing up to the fruit. It is available in most garden centers 

Tanglefoot is fine for a single-trunk tree, but not so much for bush type with low growth. I wanna kill the mound too. lol

pour some kerosene into it and light it up. That should discourage the little buggers

I've used Borax before.  It works great.  They sip it up and take it back to their nest and it kills the whole colony I think. 

So...I tried the Borax:Syrup bait. Works well. Ant problem fixed! Now about those damn fruit beetles! Just mixed 3Tbsp syrup to 1 tsp of Borax powder.
Smeared some inside a soda can with a flap cut on the side and closed it back up.
   
Put a can under each tree. Too easy!

Personally, I prefer m-80 for the mounds. It's like fourth of July any time of the year :)

I thought of this cheap method of using tape with the adhesive side out and wrapped around the tree and I stuck the overlapping ends together.I first tried 3 strips of electrical tape,but the adhesive was not sticky enough and the ants could run across it.

     I tried 2" clear tape and it appears to be sticky enough to stop the ants from going up or down the tree without getting stuck.

These are large black Carpenter ants that are normally not a problem,but with an excessive amount of rain during ripening the figs crack and the ants and bees make getting a fig to ripen more difficult.