Previous studies aiming to optimize and bundle-adjust camera poses using Neural Radiance Fields (NeRFs), such as BARF and DBARF, have demonstrated impressive capabilities in 3D scene reconstruction. However, these approaches have been designed for pinhole-camera pose optimization and do not perform well under radial image distortions such as those in fisheye cameras. Furthermore, inaccurate depth initialization in DBARF results in erroneous geometric information affecting the overall convergence and quality of results. In this paper, we propose adaptive GRUs with a flexible bundle-adjustment method adapted to radial distortions and incorporate feature-based recurrent neural networks to generate continuous novel views from fisheye datasets. Other NeRF methods for fisheye images, such as SCNeRF and OMNI-NeRF, use projected ray distance loss for distorted pose refinement, causing severe artifacts, long rendering time, and are difficult to use in downstream tasks, where the dense voxel representation generated by a NeRF method needs to be converted into a mesh representation. We also address depth initialization issues by adding MiDaS-based depth priors for pinhole images. Through extensive experiments, we demonstrate the generalization capacity of FBINeRF and show high-fidelity results for both pinhole-camera and fisheye-camera NeRFs.