Certified GKH Gardening Expert
You may need to pick the fruit before it fully ripens. While figs do not technically continue to ripen once picked, they do still soften and sweeten for a few days after they are picked, which is what you really want anyway. Try picking the fruit a just a bit before they feel ready and put them in a paper bag for a day or so after this. You should still end up with the juicy, sweet fruit you want without the ants or other bugs.
Here is an article that you may find helpful: https://www.gardeningknowhow.com/plant-problems/pests/keeping-ants-of-flowering-vines-vegetables-and-flowers.htm
Netting will help fend off birds. Here is more information: https://www.gardeningknowhow.com/edible/fruits/fegen/protect-fruit-tree-birds.htm