The space-time of the Universe is caused by de Sitter space with positive lambda. The space is fulled by vacuum with positive density ro = 3/kappa a^2, where kappa is Einstein constant, a is the radius of the Universe. The Universe in this case is the collapsar, for which Hilbert radius r_g = a. The same structure possesses neutron stars.
So can I assume that the same structure follows for black holes too because further shrinking of a neutron star will not cause any radical change to the structure of space-time?
Further, if the structure of black hole is de-Sitter, then I don't see a logical reasoning to avoid the Einstein-Rosen bridge. We can't just rule it out due to lack of evidence. Can we?
It is neither, the geometry for a single black hole is the Scwarzschild Metric (or Kerr if rotating). For a simple black hole embedded in a de-Sitter universe, you can use the McVittie metric. For more complex black holes, see this article: