New structures with favorable band structure and optical properties are of broad interest to the halide perovskite community. Recently, lead-free two-dimensional (2D) double perovskites have emerged as dimensionally reduced counterparts of their 3D analogues. Besides the structural diversity provided by the organic cation, the achievement of 2D lead-free iodide double perovskites has attached researchers to explore more structures in this new material family. Here, we report the synthesis and structures of a series of 2D iodide double perovskites based on cyclic diammonium cations (aminomethyl)piperidinium (AMP) and (aminomethyl)pyridinium (AMPY), (4AMP)2AgBiI8 and (3AMPY)2AgBiI8, and compare them with 1D structures with Bi only (x-AMP)BiI5 and (x-AMPY)BiI5 (x = 3 and 4). The crystallographic structures of the double perovskite phases are highly distorted, because of the inability of Ag to form regular octahedral coordination with iodine. The experimental bandgaps of the double perovskite phases are surprisingly similar ((4AMP)2AgBiI8) or even larger ((3AMPY)2AgBiI8) than in the 1D structures with the same cations ((4AMP)BiI5 and (3AMPY)BiI5). DFT calculations suggest that the effective electronic dimensionality of the double perovskites is on par or lower than that of 1D structures. The reduced electronic dimension of the 2D compounds originates from the weak electronic coupling between the corner-sharing Ag and Bi octahedra. The band structures for the 1D compounds are dispersive in the chain direction, suggesting that their electronic and structural dimensions are similar. Low frequency Raman spectra exhibit distinct peaks at room temperature for all compounds reported here, suggesting rigid lattices