Lets speculate a little further on what it would be like to live in a Hubble bubble. In the standard cosmological model of the Universe the structures we see today like galaxies and clusters of galaxies (and similarly the structures we don't see like the massive dark matter halos the visible matter is embedded in) formed from tiny primordial quantum fluctuations in the early universe. The fluctuations were random variations in density such that locations which were over-dense formed galaxies and those which were under-dense formed voids. It is possible, in fact statistically quite acceptable that there are voids of various sizes in the Universe. These voids would become increasingly under-dense as the Universe evolved and equivalently over-dense regions of the Universe became increasingly over-dense. Inside the void matter would expand outward due to the gravitational pull of matter in surrounding dense regions and thus an observer at the center of the void would see an accelerated expansion of matter outward. Now it is also possible that our entire observable Universe is a Hubble bubble, but that really flies in the face in all of cosmology. It is unfounded, absurd, and really the whole idea of a Hubble bubble may explain dark energy, but is hardly a very good explanation.
The Hubble Bubble is wildly speculative and precision cosmology has almost completely defeated it as a credible explanation. First, as the framework of cosmology has been successful resting on the Copernican principle it seems odd to throw it out now. It is odd and largely misguided. First, the probability of producing a void of necessary magnitude; to mimic aspects of dark energy is extremely small in the standard structure formation models. Second, the probability of an observer being at the center (the only location where the expansion effect would be noticed) is extremely low. Finally, the void would need to be close to spherical to match the observed spatial smoothness (or isotropy) of the universe. These qualitative arguments and many more quantitative arguments from precision cosmology data are laid forth in a recent paper by A. Moss, J. Zibin, and D. Scoot titled Precision Cosmology Defeats Void Models for Acceleration. The abstract follows:
The suggestion that we occupy a privileged position near the center of a large, nonlinear, and nearly spherical void has recently attracted much attention as an alternative to dark energy. Putting aside the philosophical problems with this scenario, we perform the most complete and up-to-date comparison with cosmological data. We use supernovae and the full cosmic microwave background spectrum as the basis of our analysis. We also include constraints from radial baryonic acoustic oscillations, the local Hubble rate, age, big bang nucleosynthesis, the Compton y-distortion, and for the first time include the local amplitude of matter fluctuations, σ8. These all paint a consistent picture in which voids are in severe tension with the data. In particular, void models predict a very low local Hubble rate, suffer from an "old age problem", and predict much less local structure than is observed.The paper makes several quantitative arguments against the plausibility any kind of void model for cosmic acceleration by drawing together an impressive amount of cosmological data and technical expertise, however, they don't ever mention the term Hubble Bubble. A 2007 paper by Conley et al. takes the Hubble Bubble paradigm head on: Is There Evidence for a Hubble Bubble? The Nature of Type Ia Supernova Colors and Dust in External Galaxies. In Conley et al. they explore how dust effects the colors of type Ia supernovae because they reason if the dust can be modeled as a purely local Milky Way effect then the supernovae data would actually favor the Hubble Bubble. Of course, despite difficulties the analysis, they find that in their parametrization there is evidence for more than the simply effect of local Milky Way dust implying doom for the Hubble Bubble. So the Hubble Bubble has been burst.
Adam Moss, James P. Zibin, & Douglas Scott (2010). Precision Cosmology Defeats Void Models for Acceleration arXiv preprint arXiv: 1007.3725v1
Conley, A., Carlberg, R., Guy, J., Howell, D., Jha, S., Riess, A., & Sullivan, M. (2007). Is There Evidence for a Hubble Bubble? The Nature of Type Ia Supernova Colors and Dust in External Galaxies The Astrophysical Journal, 664 (1) DOI: 10.1086/520625