There's lots of 4 saddle bridges that can accommodate either top loading or string thru with the holes pre-drilled in the baseplate. If money's no object and you want a superior bridge, get a Babicz. Some Badass bridges also are a good option. I think Hipshot has some as well. You can find cheaper options for imported bridges on eBay, and I've bought a few there. You can also drill holes in the baseplate of almost any style for string thru, which I've also done a few times. I guess you could also pass through the holes in the back of the baseplate and then go down through the body, but you would need to install ferrules both on the top and back of the body. I've never done this but some of the Gibson style bridges are done this way.
When I drill the body, I use the holes in the bridge baseplate as a template to start drilling the holes from the top, but only go part way through the body. Then I remove the bridge, and then use a board with the smooth end of a broken drill bit the same size as the hole, centered on the drill press base, flip the bpdy over and use the broken bit as a guide pin to line up the hole on the back directly in line with the hole in the bridge, and then finish drilling the hole. You can find some Youtube videos showing this method. The holes in the back will be nice and straight this way.
There's different length ferrules available. I find that standard long scale strings work with a 34" scale bass with regular ferrules, but you can install longer ferrules that protrude deeper in the body if you like.
Pics below aren't zoomed into the bridges, but I think you can see enough to get an idea of some options.
Here's a bass with a fender-style bridge from eBay with both top loading and string thru capability.
Here's a different style bridge with top loading and string loading capability.
Here's a Fender-style bridge drilled to add string thru capability.
Here's a Fender hi-mass bridge (similar to a Badass) drilled for string thru.
Here's a Gibson copy that is kind of similar to your idea of passing the strings all the way through the bridge and then going down into the body behind the bridge.
When I drill the body, I use the holes in the bridge baseplate as a template to start drilling the holes from the top, but only go part way through the body. Then I remove the bridge, and then use a board with the smooth end of a broken drill bit the same size as the hole, centered on the drill press base, flip the bpdy over and use the broken bit as a guide pin to line up the hole on the back directly in line with the hole in the bridge, and then finish drilling the hole. You can find some Youtube videos showing this method. The holes in the back will be nice and straight this way.
There's different length ferrules available. I find that standard long scale strings work with a 34" scale bass with regular ferrules, but you can install longer ferrules that protrude deeper in the body if you like.
Pics below aren't zoomed into the bridges, but I think you can see enough to get an idea of some options.
Here's a bass with a fender-style bridge from eBay with both top loading and string thru capability.
Here's a different style bridge with top loading and string loading capability.
Here's a Fender-style bridge drilled to add string thru capability.
Here's a Fender hi-mass bridge (similar to a Badass) drilled for string thru.
Here's a Gibson copy that is kind of similar to your idea of passing the strings all the way through the bridge and then going down into the body behind the bridge.
