With the rapid progress on perovskite (PVK) and bifacial solar cells, there is a huge interest in integrating PVK with established technologies such as crystalline silicon (c-Si) and GIGS for bifacial tandem structures. Here we use self-consistent optical/electrical simulations to compare various stack/terminal configurations for bifacial tandem solar cells having PVK as the top cell. In particular, we compare a non-conventional three-terminal four-junction (3T-4J) twin bifacial tandem configuration with standard two-junction bifacial tandem structures having a monolithic two-terminal (2T-2J) or mechanically stacked four-terminal (4T-2J) integration. We show that the optimal design of 2T-2J cell is strongly albedo dependent - the cell designed for a given albedo will perform sub-optimally for other albedo due to the current-matching constraint. A mechanically stacked 4T-2J cell, on the other hand, can perform optimally for a broad range of albedo, albeit at the cost of additional processing complications. The 3T-4J twin tandem cell could offer a relatively simpler process through back-toback bonding of two identical monolithic 2J tandem cells with superior utilization of albedo in a broad range. The potential benefit of 3T-4J cell could however be limited due to a high front reflection, hence necessitating anti-reflection approaches. We further quantify the effect of bottom subcell material on the efficiency for PVK tandem cells. Using state-of-the-art bottom subcells, efficiency of 33% and 30% respectively could be achieved at the average Earth albedo of similar to 30%. By integrating advanced anti-reflectance techniques, the absolute cell efficiency could further be improved by similar to 4%.