The routing depth for all tremolos is always 1" deep.
The picture below shows the route for a stud mount. The main route in the center is the same whether it a stud mount or flat mount. The difference in routes is simply the studs and bridge posts versus 4 wood screws used on flat mounts. On another note: most basses need to have the tremolo or bridge countersunk into the body to achieve the right action and string angle.
There are 2 different mounting styles: TOM or Flat mounting as seen below.
If you have a Tune-o-Matic or TOM bridge (above, left), whether the body is flat topped or not, you'll want the stud mount type Kahler (above, middle). The Kahler stud mount system has 2 hooks on the side of the frame. These hooks will go around the studs just like the stop tail piece does on the Tune-o-Matic and mount up like on the Les Paul (below). Flat mounting tremolos are generally square shaped and use four wood screws for installation and the unit is simply screwed down to the flat body top over the routed cavity. (above, right)
SPECIAL NOTE: In the 80's, Gibson's and most guitars with Tune-o-Matic bridges, had a standardized installation location that was programmed into the routing machines at the factory and in those days, Kahlers were a drop on perfect installation. But since the late 80's - early 90's, the stop tail part of the Tune-o-Matic bridge has been shifted around like the grills on a Chevy over the years. The bridge part is always in the same place for the scale range of course, but the tail piece is not as important. It can go anywhere since all it does is hold the strings. Unfortunately the Kahler needs these studs to mount on and since they are no longer in a standardized locale, the studs sometimes need to be removed and relocated in the right spot. You need about 2-1/16" to about 2-1/4" between the bridge sections small E saddle notch (which should be set to the scale length) and the center/middle of the stop tail piece to be "in the ballpark" for mounting a six string stud mount system without having to relocate the studs. If you have the one piece wrap-around Uni-Matic, then you don't have a problem with relocation. This step can be skipped since you will be drilling fresh new holes for the rear studs and the install will look perfect. I always suggest a qualified Luthier to do the job.