+1 on the Titebond. Do NOT use Gorilla glue - Gorilla glue expands, and your bridge will never end up in the right place - you will ruin the guitar!
I own a music school, and we do some repair work. At the moment I am working on exactly the same repair. As LessPaul said, you need to hit the exact spot. You also need to make sure the bottom of the bridge and the top of the guitar mate perfectly - this kind of damage happens when the top is bellying (curving upwards in the center) a bit, and the bridge isn't - that creates a tension that over time breaks the glue joint.
In my opinion it's not a great DIY project unless you're willing to take considerable risk of not having a playable instrument at the end. If you are willing to take the risk, you're also going to need clamps with a deep enough throat to secure the bridge while the glue dries and a bridge caul to evenly distribute the pressure from the clamps across the bridge. (If you're handy, make the caul)
Getting the bridge to mate with the top is important to prevent it from happening again. Some people use special clamps to flatten the top, but in most cases I think it's a better fix to shape the bottom of the bridge. I do this by putting sandpaper on the top of the guitar, face up, and work the bridge across the sandpaper - you're using the top as a form (make sure you don't move the bridge too much, and the motion needs to be in line with the neck, not side-to-side)
If I get a chance I'll take some pics of the repair in progress so you can see what I'm describing.
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Edit: Here are pictures:
1. The guitar with the bridge removed, and the splintering cleaned up:
https://imgur.com/YDjx76S
2. With a straightedge you can see the bellying of the top:
https://i.imgur.com/ssgWGDo.jpg
3. The bellying means the joint will have tension/be weak where the surfaces don't mate:
https://i.imgur.com/y7hGS8N.jpg
4. Sanding to mate the surfaces - this is where I am with it this morning. Repair will be complete next week - I'll take some pictures of the caul/clamp process as I get there.
https://i.imgur.com/GnhfdmY.jpg
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Edit #2 - three more pictures
https://imgur.com/a/TDA7v
5. Using a caul for gluing is important to get even clamping pressure. There are some fancy ones available, but I just use wood to build up a caul to match the profile of the bridge. The first pictures shows the cut pieces laid out on the bridge for test fitting, and the second picture is the pieces stacked to form the caul.
6. You'll need a clamp with a sufficient throat to reach the bridge - at least 4". Some people use multiple clamps, but if your caul fits the bridge properly you can get away with just one (which simplifies getting even clamping pressure). The third picture in this set shows the bridge clamped.
