There are a couple of options... If you wanted to really do it proper, I'd recommend removing the bridge entirely and either getting a new one or removing as much of the old glue as possible and re-gluing it.
If the instrument doesn't have great value to you and you just want it in good working order again in a way that should last, I'd just re-glue and clamp it.
It's a little hard to tell, but it looks like it's wood on wood. If this is the case, I'd recommend hide glue or Titebond.
Both will work. Hide glue is more traditional. Though, it is an animal product, just in case that's a concern.
Titebond is easier to work with, but maybe a bit harder to remove down the road.
Personally, I'd recommend Titebond. It's easy to use and the fact that you can buy it just about anywhere is nice.
If the bridge itself is separating, you could try just swabbing glue into the separated area as well, it should go back together ok when clamped properly.
For clamping the bridge down, if you can fit them in the sound hold, use 2 clamps so that you'll get even pressure and connection between the bridge and body. You could also fairly easily rig up something like this... http://farm3.static.flickr.com/2085/2412687254_f8e311629f.jpg