It will fit, HOWEVER I'd like to share my recent experience with a Badass II bridge on it. I recently acquired a '76 Precision. I thought the bass sounded decent, but was pretty generic and didn't really seem to have much variance in tone despite a lot of knob twiddling on the amp and with the bass's tone control. My amp sounded pretty plain, too and the P-bass tone just wasn't there. Since the bass was in such immaculate condition and everything was original except for the bridge and pup, I decided to bring her back to as near to original condition as I could. First thing I did was replace the BAdass II bridge with the same bridge that comes on the '62 AVRI, and still had the same Dimarzio pup in the bass. I could not believe how differren't the tone was with just getting rid of the BAII. The bass came alive, had more growl, roundness, character, personality, and actually sounded like a P-bass! tone controls on the amp and bass were way more responsive as well. The only noticeable thing was the sustain was not as good, but seriously, this is not a characteristic (at least to me) that is worth sacrificing all of the tonal characteristics that make a Precision bass a Precision bass. Now my entire bass actually vibrates and resonates so much that I can feel it through the entire body and neck. With the BAII it prevented that from happening. Of course everyone's tonal needs, opinions, and what is pleasing to them is different, and you may love the BAII. I'm going to be selling mine. The $30 Fender bridge is my favorite over the BAII. I'd sell the BAII and put it toward a nice peal or some other gear that would be more beneficial as opposed to a giant piece of metal that will kill the inherent tone of your instrument!
I believed in the switch back to stock so much I even started a thread about it a few days ago:
http://www.talkbass.com/forum/f8/my-1976-precision-before-after-pics-958210/