That is a video of Gary installing an Upton Rev Solo. He's using a combination of a rasp, file, and sandpaper on a block. The file and sandpaper you should be able to find at just about any hardware store, the rasp you might have to go somewhere a little more woodworking orientated such as Woodcraft, Lee Valley, etc. You really don't need a rasp. It removes the material much more quickly, which could easily mean you go too far. Obviously the whole "measure twice, cut once" saying comes into play, or in this case something more like "take a bit at a time and check often" doesn't have the same ring to it, but you get the point. I do not know the Bass Max personally, so I could not suggest if it would benefit from the "hot spot" that Gary talks about, where the wing and leg of the bridge are slightly rounded so there is a smaller contact surface, or if you want to keep the surfaces as parallel as possible for a larger contact area.
If you are careful and slow about fitting it, make sure to check frequently that the gap you are creating is not too large but also you aren't creating any really weird angles, sharp edges, etc. then you can likely do it on your own fairly successfully. I would recommend putting a towel or something else around the bridge foot and over the bass so if you drop the file you don't leave a mark on the instrument or if you're using a small enough file you don't have to try to fish it out of the f hole. If you decide you really want to use a rasp, you will want to be careful about tear out depending on how aggressive it is, and you will want to finish with some sandpaper on a block so you have a more smooth surface.
The real danger of doing it yourself is over doing it. If you go too far and take away too much, then it isn't going to fit. If that is the case you might be sunk for using that particular type of pickup, and either have to consider something else, or start again with a new bridge. Harder to do if you are using something like 150-300 sandpaper on a block than a knife or a rasp, but still possible.