We now know of course that a quasar is the central region of a galaxy, powered by an especially active accretion disk around the supermassive black hole. But this activity is not unique to the most distant galaxies, or to quasars. Blazars, quasars, radio galaxies and Seyferts are all powered in the exact same way. In general we refer to these as "active galaxies", with an "active galactic nucleus" or AGN. It wasn't realized until fairly recently that all these different things are actually the same kind of object. The difference in what we see and classify them as just depends on our viewing angle:
In other words, different types of active galaxies are the same things as quasars. Or, quasars are AGN seen at a particular viewing angle.
So we can ask, "Was the Milky Way ever an active galaxy?" Definitely! We do see the evidence left behind from previous activity like you mention with the fast-moving bubbles and shocks. I think it is unlikely that this event was so luminous that it would dominate over all the starlight of the galaxy, but astronomers in nearby galaxies would be able to tell.
Another near certainty is that it will become active again in the future, especially with the merger with M31!
Also, are these "bubbles" of pressure created by the gas responsible for the creation of arms in a spiral galaxy? Kind of like tree-rings, multiple arms might mean multiple Quasar stages or periods of time?
No, the effect of these ejections is mostly to remove gas from the galactic center, and especially to blow it out in polar outflows. This mechanism is very important for regulating the black hole's growth, and also plays a part in a dynamical relationship between the black hole's mass and the properties of the galactic bulge, like the M-Sigma relation. But the gas in these ejections is too thin and lacks the oomph to be able to set up the spiral structure throughout the disk.
The spiral arms are instead generated by density waves, which move slower than the material of the disk itself. As dust and gas pass through a density wave they get compressed, triggering star formation and the arm structure we observe. (This is a very good model for "grand design" spirals). In computer simulations we also sometimes see the star formation process itself become self-propagating and lead to spiral structure. Gravitational perturbations from mergers or neighboring galaxies can also play a role.
So in short there are a lot of mechanisms behind spiral formation, and nature probably uses a combination of them. But the central black hole probably has little to do with it, even though it does have significant and surprising influences on other large features of the galaxy.