I sometimes anchor my hand on the bridge also when playing with a pick. You end up with a trebly sound because of picking so near the bridge - I like that sound, it's one of my favorite pick techniques! Sounds particularly great with a "P" pickup.
IME a bridge with big roll saddles like the "classic" fender bridge is much less than optimal, and you can mess up height, intonation, all kinds of stuff. You want something with more substance to it where you put your hand, which will not move around and you won't unintentionally change settings!
In my experience, the classic Schaller Roller bridge is an outstanding piece for this particular pick technique. I've had three basses with that bridge in one form or another and it is quite a good piece. However, as it is not a 5 screw "drop-in" replacement for the Fender, it will require drilling to install.
The Gotoh is not a good choice, the saddles are so similar to the Fender. The Badass is better, but still may have height adjust screws sticking up, which I personally don't like. I'll bet an ABM bridge would be great, but they're very expensive!