Nested skyrmion bags are composite magnetic solitons whose internal occupation numbers provide an expanded state space for multilevel information encoding. However, deterministic and region-selective writing of individual skyrmions into nested bags remains challenging. Here, using micromagnetic simulations, we propose a field-gated nanocontact protocol for generating and programming double-layer nested skyrmion bags S(m,S(n)). The protocol exploits the opposite field responses of bag regions with antiparallel magnetic backgrounds. Spatially segmented perpendicular magnetic fields selectively expand either the outer region or the inner bag until it overlaps with a nanocontact. A spin-polarized current pulse of the appropriate polarity then nucleates one skyrmion in the selected region, while subsequent field-driven contraction moves the written skyrmion away from the contact and restores the writing site for repeated operation. Starting from an empty nested bag S(0,S(0)), this procedure enables the controlled construction of S(m,S(0)), S(0,S(n)), and general S(m,S(n)) states. The simulated total topological charge changes in unit steps during sequential writing, confirming one-at-a-time and region-selective control. These results provide a possible route toward programmable nested topological states for multilevel spintronic information encoding.