As to the hip bridging... I would have said hip-bridging is in Bujinkan Budo Taijutsu (as Sensei is pretty relaxed on control of Budo Taijutsu - allowing freedom to change and add as necessary...). You can probably take the Kihon Happo and use the "henka" card to attach to practically ANY Martial Arts move... The question comes down to which of the 9 traditions did the "bridging" come from (and then is *your* version of bridging the historically accurate one?)?
I would argue back that whether "hip bridging" or "shrimping" or anything like that is "in Bujinkan Budo Taijutsu" has less to do with which tradition it supposedly comes from, and more to do with the *WAY* the body is used to accomplish it.
One can clearly do shrimping in ways that conflict with the teachings of Hatsumi-sensei, just as one can do shrimping in ways that mesh with them.
(Heck, I would argue that Hatsumi-sensei has been doing movements at Ayase that some would label as "hip bridging" and "shrimping" since before the whole Gracie Jiu-jutsu boom took off. Again, what is important is the way in which the movement is performed.)
I personally make students do a kind of "shrimping" for several months so they can learn the proper way of rotating the hips, but this "shrimping" is definitely different from the stuff I've seen on groundfighters.
I do this because the mechanics of shrimping can be used to isolate certain body parts, which, in turn, forces the student to learn certain movements in certain ways. I have used "Bujinkan shrimping methods" to teach students how to improve their power generation in striking, for example....
For some, the idea of using a "groundfighting move" to teach "standing striking" may sound strange. But if you spend time breaking down the skeletal movements, you will see that shrimping and striking are actually quite complementary to each other.
This is why it is so important to know "what is Taijutsu" and "what is not Taijutsu" before you start experimenting with such things. Otherwise, you could create anti-Taijutsu habits that lead you *VERY* far from the BBT path.
Once you get too far away, you literally will no longer be able to see what Hatsumi-sensei is doing.... And once that happens, it's really hard to get back on the path. You simply cannot see anything anymore!
-ben